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A078027 Expansion of (1-x)/(1-x^2-x^3). 11
1, -1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, 97229, 128801, 170625, 226030, 299426 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

Table of n, a(n) for n=0..53.

P. Chinn and S. Heubach, Integer Sequences Related to Compositions without 2's, J. Integer Seqs., Vol. 6, 2003.

Index entries for linear recurrences with constant coefficients, signature (0, 1, 1).

FORMULA

a(n) is asymptotic to r^(n-2) / (2*r+3) where r = 1.3247179572447..., the real root of x^3 = x + 1 . For n>=4, a(n) = a(n-2) + a(n-3) . - Philippe Deléham, Jan 13 2004

PROG

(PARI) Vec((1-x)/(1-x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

CROSSREFS

The following are basically all variants of the same sequence: A000931, A078027, A096231, A124745, A133034, A134816, A164001, A182097, A228361 and probably A020720. However, each one has its own special features and deserves its own entry.

Sequence in context: A124745 A133034 A000931 * A134816 A228361 A182097

Adjacent sequences:  A078024 A078025 A078026 * A078028 A078029 A078030

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified March 28 07:54 EDT 2017. Contains 284182 sequences.