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
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).
Crossrefs
First differences of A023437.
Programs
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Magma
m:=40; R
:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^2-x^3-x^4-x^5-x^6))); // Vincenzo Librandi, Jun 24 2013 -
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 *) -
PARI
Vec(1/(1-x^2-x^3-x^4-x^5-x^6)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
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
Comments