A013982 Expansion of 1/(1-x^2-x^3-x^4-x^5).

1, 0, 1, 1, 2, 3, 4, 7, 10, 16, 24, 37, 57, 87, 134, 205, 315, 483, 741, 1137, 1744, 2676, 4105, 6298, 9662, 14823, 22741, 34888, 53524, 82114, 125976, 193267, 296502, 454881, 697859, 1070626, 1642509

Offset

0,5

Comments

Number of compositions of n into parts p where 2 <= p < = 5. [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

J. D. Opdyke, A unified approach to algorithms generating unrestricted.., J. Math. Model. Algor. 9 (2010) 53-97, Table 7

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

Formula

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

Mathematica

CoefficientList[Series[1/(1-x^2-x^3-x^4-x^5), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 1, 1, 1, 1}, {1, 0, 1, 1, 2}, 40] (* Harvey P. Dale, Sep 19 2011 *)

Prog

(PARI) Vec(1/(1-x^2-x^3-x^4-x^5)+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))); // Vincenzo Librandi, Jun 24 2013

Crossrefs

Sequence in context: A159288 A363958 A033320 * A202411 A293161 A235648

Adjacent sequences: A013979 A013980 A013981 * A013983 A013984 A013985

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved