%I #10 Feb 02 2024 09:25:30

%S 1,0,0,0,1,0,0,1,1,0,0,2,1,0,1,3,1,0,3,4,1,1,6,5,1,4,10,6,2,10,15,7,6,

%T 20,21,9,16,35,28,15,36,56,37,31,71,84,52,67,127,121,83,138,211,173,

%U 150,265,332,256,288,476,505,406,553,808,761,694,1029,1313,1167,1247,1837,2074,1861,2276,3150,3241

%N Expansion of 1/(1 - x^4 - x^7).

%C Number of compositions of n into parts 4 and 7.

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

%F a(n) = a(n-4) + a(n-7).

%o (PARI) my(N=80, x='x+O('x^N)); Vec(1/(1-x^4-x^7))

%o (PARI) a(n) = sum(k=0, n\7, ((n-3*k)%4==0)*binomial((n-3*k)/4, k));

%Y Cf. A005709, A017847, A369813, A369814, A369816.

%K nonn,easy

%O 0,12

%A _Seiichi Manyama_, Feb 02 2024