%I #13 Feb 02 2024 09:25:33
%S 1,0,0,1,0,0,1,1,0,1,2,0,1,3,1,1,4,3,1,5,6,2,6,10,5,7,15,11,9,21,21,
%T 14,28,36,25,37,57,46,51,85,82,76,122,139,122,173,224,204,249,346,343,
%U 371,519,567,575,768,913,918,1139,1432,1485,1714,2200,2398,2632,3339,3830,4117,5053,6030,6515,7685
%N Expansion of 1/(1 - x^3 - x^7).
%C Number of compositions of n into parts 3 and 7.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,0,0,0,1).
%F a(n) = a(n-3) + a(n-7).
%o (PARI) my(N=80, x='x+O('x^N)); Vec(1/(1-x^3-x^7))
%o (PARI) a(n) = sum(k=0, n\7, ((n-4*k)%3==0)*binomial((n-4*k)/3, k));
%Y Cf. A005709, A017847, A369813, A369815, A369816.
%K nonn,easy
%O 0,11
%A _Seiichi Manyama_, Feb 02 2024
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