A013983 Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6).

1, 0, 1, 1, 2, 3, 5, 7, 12, 18, 29, 45, 71, 111, 175, 274, 431, 676, 1062, 1667, 2618, 4110, 6454, 10133, 15911, 24982, 39226, 61590, 96706, 151842, 238415, 374346, 587779, 922899, 1449088, 2275281, 3572527

Offset

0,5

Comments

Number of compositions of n into parts p where 2 <= p < = 6. [Joerg Arndt, Jun 24 2013]

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

R. Mullen, On Determining Paint by Numbers Puzzles with Nonunique Solutions, JIS 12 (2009) 09.6.5.

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

Formula

a(n) = a(n-6) + a(n-5) + a(n-4) + a(n-3) + a(n-2). - Jon E. Schoenfield, Aug 07 2006

G.f.: 1 / ( (1+x)*(1-x^5-x^3-x)). a(n)+a(n+1) = A060961(n). - R. J. Mathar, Mar 22 2011

Mathematica

CoefficientList[Series[1 / (1 - x^2 - x^3 - x^4 - x^5 - x^6), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 23 2013 *)
LinearRecurrence[{0, 1, 1, 1, 1, 1}, {1, 0, 1, 1, 2, 3}, 50] (* Harvey P. Dale, Dec 31 2013 *)

Prog

(PARI) Vec(1/(1-x^2-x^3-x^4-x^5-x^6)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^2-x^3-x^4-x^5-x^6))); // Vincenzo Librandi, Jun 24 2013

Crossrefs

First differences of A023437.

Sequence in context: A048808 A263358 A239915 * A257863 A169986 A218021

Adjacent sequences: A013980 A013981 A013982 * A013984 A013985 A013986

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved