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a(n) = Sum_{k=0..floor(n/4)} binomial(floor(k/3),n-4*k).
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%I #10 Oct 01 2024 07:22:05

%S 1,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,2,1,0,1,2,1,0,1,2,

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

%U 10,6,6,10,10,6,7,15,20,16,12,16,20,16,12,16,20,16,13,22,35,36

%N a(n) = Sum_{k=0..floor(n/4)} binomial(floor(k/3),n-4*k).

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,1,1).

%F G.f.: (1-x^12)/((1-x^4) * (1-x^12-x^13)) = (1+x^4+x^8)/(1-x^12-x^13).

%F a(n) = a(n-12) + a(n-13).

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

%o (PARI) my(N=90, x='x+O('x^N)); Vec((1+x^4+x^8)/(1-x^12-x^13))

%Y Cf. A079398, A376649.

%K nonn,easy

%O 0,26

%A _Seiichi Manyama_, Oct 01 2024