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

%I

%S 1,0,1,1,2,3,5,7,12,18,29,45,71,111,175,274,431,676,1062,1667,2618,

%T 4110,6454,10133,15911,24982,39226,61590,96706,151842,238415,374346,

%U 587779,922899,1449088,2275281,3572527

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

%C Number of compositions of n into parts p where 2 <= p < = 6. [_Joerg Arndt_, Jun 24 2013]

%H Vincenzo Librandi, <a href="/A013983/b013983.txt">Table of n, a(n) for n = 0..1000</a>

%H R. Mullen, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Mullen/mullen2.html">On Determining Paint by Numbers Puzzles with Nonunique Solutions</a>, JIS 12 (2009) 09.6.5

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,1,1).

%F a(n) = a(n-6) + a(n-5) + a(n-4) + a(n-3) + a(n-2). - _Jon E. Schoenfield_, Aug 07 2006

%F G.f. 1 / ( (1+x)*(1-x^5-x^3-x)). a(n)+a(n+1) = A060961(n). - _R. J. Mathar_, Mar 22 2011

%t CoefficientList[Series[1 / (1 - x^2 - x^3 - x^4 - x^5 - x^6), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 23 2013 *)

%t LinearRecurrence[{0,1,1,1,1,1},{1,0,1,1,2,3},50] (* _Harvey P. Dale_, Dec 31 2013 *)

%o (PARI) Vec(1/(1-x^2-x^3-x^4-x^5-x^6)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%o (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

%Y First differences of A023437.

%K nonn,easy

%O 0,5

%A _N. J. A. Sloane_.

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Last modified June 15 21:52 EDT 2021. Contains 345053 sequences. (Running on oeis4.)