The Encyclopedia of Integer Sequences

Description

This encyclopedia contains more than 5000 integer sequences, over half of which have never before been catalogued. Because the sequences are presented in the most natural form, and arranged for easy reference, this book is easier to use than the authors earlier classic A Handbook of Integer Sequences. The Encyclopedia gives the name, mathematical description, and citations to literature for each sequence. Following sequences of particular interest, thereare essays on their origins, uses, and connections to related sequences (all cross-referenced). A valuable new feature to this text The initial chapters are both amusing and enlightening. They serve as a delightful introduction to the subject and a short course on how to identify and work with integer sequences. This encyclopedia brings Sloanes ground-breaking Handbook up to date, more than doubling its size, and linking both the old and the new material to an extensive bibliography (over 25 pages long), of current and classic references. An index to all the sequences in the book is also available separately on disk in Macintosh and IBM formats. Title Page Contents Preface Abbreviations Chapter 1. Descrption of the book 1.1 Descrption of a typical entry 1.2 Arrangement of table 1.3 Number of terms given 1.4 References 1.5 What sequences are included? 1.6 The figures Chapter 2. How to handle a strange sequence 2.1 How to see if a sequence is in the table 2.2 If the sequence is not in the table 2.3 Finding the next term 2.4 Recurrences and generating functions 2.5 Analysis of differences 2.6 Other methods for hand analysis 2.7 Transformations of sequences 2.8 Methods for computer investigation of sequences 2.9 The on-line versions of the Encyclopedia 2.10 The floppy disk Chapter 3. Further topics 3.1 Applications 3.2 History 3.3 Differences from the 1973 book 3.4 Future plans 3.5 Acknowledgments The table of sequences SEQUENCES OF 0's AND 1's [M0000] SEQUENCES BEGINNING ..., 2, 0, ... [M0004] SEQUENCES BEGINNING ..., 2, 1, ... [M0040] Figure M0062. ALIQUOT SEQUENCES Figure M0126. LINUS AND SALLY SEQUENCES Figure M0180. NON-ATTACKING QUEENS. SEQUENCES BEGINNING ..., 2, 2, ... [M0185] Figure M0240. ERROR-CORRECTING CODES Figure M0320. SERIES-REDUCED TREES SEQUENCES BEGINNING ..., 2, 3, ... [M0394] Figure M0436. SELF-GENERATING SEQUENCES Figure M0500. EULER TOTIENT FUNCTION Figure M0557. ULAM SEQUENCES Figure M0663. PARTITIONS Figure M0692. FIBONACCI AND LUCAS NUMBERS Figure M0791. TREES Figure M0847. KNOTS SEQUENCES BEGINNING ..., 2, 4, ... [M0928] Figure M0982. ORCHARD PROBLEM Figure M1040. LIGHT-BULB GAME Figure M1041. SLICING A PANCAKE Figure M1141. RNA MOLECULES Figure M1197. GEOMETRIES Figure M1253. GRAPHS SEQUENCES BEGINNING ..., 2, 5, ... [M1311] Figure M1332. BEATTY SEQUENCES Figure M1369. UNCROSSED KNIGHT'S TOURS Figure M1459. CATALAN NUMBERS Figure M1495. PARTIALLY ORDERED SETS SEQUENCES BEGINNING ..., 2, 6, ... [M1556] Figure M1645. PASCALS TRIANGLE Figure M1722. MULTIPLICATIVE ENCODING OF ARRAYS SEQUENCES BEGINNING ..., 2, 7, ... [M1727] SEQUENCES BEGINNING ..., 2, 8, ... [M1822] Figure M1845. POLYOMINOES SEQUENCES BEGINNING ..., 2, 9, ... [M1910] Figure M1937. DERANGEMENTS SEQUENCES BEGINNING ..., 2, 10, ..., ..., 2, 11, ... [M1958] Figure M2051. HARD SEQUENCES SEQUENCES BEGINNING ..., 3, 0, ...TO..., 3, 3, ... [M2192] Figure M2209. SPHERE-PACKING PROBLEM Figure M2218. DECIMAL EXPANSIONS SEQUENCES BEGINNING ..., 3, 4, ...TO..., 3, 7, ... [M2297] Figure M2336. THETA SERIES OF HEXAGONAL LATTICE Figure M2375. DISSECTIONS Figure M2497. CELLULAR AUTOMATA Figure M2535. POLYGONAL NUMBERS Figure M2540. GOLOMB RULERS Figure M2566. PLANAR PARTITIONS Figure M2629. OUR FAVORITE SEQUENCES Figure M2671. MAPPINGS ON AN n-SET SEQUENCES BEGINNING ..., 3, 8, ...TO..., 3, 12, ... [M2709] Figure M2817. TOPOLOGIES (See Fig. M3032.) Only 8 terms of this sequence are known. SEQUENCES BEGINNING ..., 3, 13, ...,..., 3, 14, ... [M2938] Figure M3032. RELATIONS Figure M3097. CONTINUED FRACTIONS SEQUENCES BEGINNING ..., 4, 0, ...TO..., 4, 12, ... [M3183] Figure M3218. THETA SERIES Figure M3224. ATTACKING KNIGHTS Figure M3382. PYRAMIDAL NUMBERS Figure M3416. EULER'S TRIANGLE SEQUENCES BEGINNING ..., 4, 13, ...,..., 4, 14, ... [M3460] SEQUENCES BEGINNING ... 5, ... [M3727] Figure M3736. HADAMARD MATRICES Figure M3826. CENTERED POLYGONAL NUMBERS Figure M3860. NECKLACES, POLYNOMIALS Figure M3987. QUARTERING A CHESSBOARD Figure M4019. EULER, TANGENT, GENOCCHI NUMBERS SEQUENCES BEGINNING ... 6, ... [M4040] Figure M4189. BERNOULLI NUMBERS Figure M4299. HARMONIC NUMBERS SEQUENCES BEGINNING ..., 7, ... [M4319] SEQUENCES BEGINNING ..., 8, ... AND ..., 9, ... [M4466] Figure M4482. SQUARING A SQUARE Figure M4587. FOLDING STAMPS, MEANDERS SEQUENCES BEGINNING ..., 10, ...TO..., 13, ... [M4674] Figure M4730. PERMUTATIONS, STIRLING NUMBERS OF 1ST KIND Figure M4822. DISALLOWED SEQUENCES SEQUENCES BEGINNING ..., 14, ...TO..., 24, ... [M4921] Figure M4981. STIRLING NUMBERS OF 2ND KIND, BELL NUMBERS Figure M5140. 24-CELL SEQUENCES BEGINNING ..., 25, ... ONWARDS Figure M5405. SILLY SEQUENCES Bibliography [AABB] [AMN] [BAMS] [BO47] [CaRo91] [CO89] [DE87] [EG80] [FPSAC] [GK68] [GU58] [Henr67] [IDM] [jm] [Kimu94b] [LE77] [Lunn74] [MO68] [NMT] [PE79] [PoRu94] [rhb] [SA81] [SIAJ] [ST70] [TO72] [WIEN] Index A, B C D E F G H I, J K, L M N, O, P Q, R S T U, V, W X, Y, Z, 1-3