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Expansion of 1/(1 - x^5 - x^7).
5

%I #15 Jul 03 2024 04:48:53

%S 1,0,0,0,0,1,0,1,0,0,1,0,2,0,1,1,0,3,0,3,1,1,4,0,6,1,4,5,1,10,1,10,6,

%T 5,15,2,20,7,15,21,7,35,9,35,28,22,56,16,70,37,57,84,38,126,53,127,

%U 121,95,210,91,253,174,222,331,186,463,265,475,505,408,794,451,938,770,883,1299,859,1732,1221

%N Expansion of 1/(1 - x^5 - x^7).

%C Number of compositions of n into parts 5 and 7.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1,0,1).

%F a(n) = a(n-5) + a(n-7).

%F Gf.: 1/((1-x+x^2)*(1+x-x^3-x^4-x^5)) . - _R. J. Mathar_, Jul 03 2024

%o (PARI) my(N=80, x='x+O('x^N)); Vec(1/(1-x^5-x^7))

%o (PARI) a(n) = sum(k=0, n\7, ((n-2*k)%5==0)*binomial((n-2*k)/5, k));

%Y Cf. A005709, A017847, A369813, A369814, A369815.

%K nonn,easy

%O 0,13

%A _Seiichi Manyama_, Feb 02 2024