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%I #27 Feb 02 2024 09:02:57
%S 1,0,0,0,0,0,1,1,0,0,0,0,1,2,1,0,0,0,1,3,3,1,0,0,1,4,6,4,1,0,1,5,10,
%T 10,5,1,1,6,15,20,15,6,2,7,21,35,35,21,8,9,28,56,70,56,29,17,37,84,
%U 126,126,85,46,54,121,210,252,211,131,100,175,331,462,463,342,231,275,506,793,925
%N Expansion of 1/(1-x^6-x^7).
%C Number of compositions of n into parts 6 and 7. - _Joerg Arndt_, Jun 27 2013
%H Harvey P. Dale, <a href="/A017847/b017847.txt">Table of n, a(n) for n = 0..1000</a>
%H Johann Cigler, <a href="https://arxiv.org/abs/2212.02118">Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials</a>, arXiv:2212.02118 [math.NT], 2022.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1,1).
%F a(0)=1, a(1)=0,a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=1; for n>6, a(n) = a(n-6)+a(n-7). - _Harvey P. Dale_, Dec 15 2012
%t CoefficientList[Series[1/(1-x^6-x^7), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 1, 1}, {1, 0, 0, 0, 0, 0, 1}, 70] (* _Harvey P. Dale_, Dec 15 2012 *)
%t CoefficientList[Series[1 / (1 - Total[x^Range[6, 7]]),{x, 0, 70}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)
%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^6-x^7))); /* or */ I:=[1,0,0,0,0,0,1]; [n le 7 select I[n] else Self(n-6)+Self(n-7): n in [1..70]]; // _Vincenzo Librandi_, Jun 27 2013
%Y Column k=6 of A306713.
%K nonn,easy
%O 0,14
%A _N. J. A. Sloane_.
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