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A376695 a(n) = Sum_{k=0..floor(n/2)} binomial(n-2*k,floor(k/3)).

%I A376695 #11 Oct 02 2024 07:52:11
%S A376695 1,1,2,2,3,3,3,4,5,7,9,12,15,18,22,27,34,43,55,70,88,110,137,171,214,
%T A376695 269,339,427,537,674,845,1059,1328,1667,2094,2631,3305,4150,5209,6537,
%U A376695 8204,10298,12929,16234,20384,25593,32130,40334,50632,63561,79795,100179,125772,157902,198236
%N A376695 a(n) = Sum_{k=0..floor(n/2)} binomial(n-2*k,floor(k/3)).
%H A376695 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1).
%F A376695 G.f.: (1-x^6)/((1-x^2) * (1-x*(1+x^6))) = (1+x^2+x^4)/(1-x*(1+x^6)).
%F A376695 a(n) = a(n-1) + a(n-7).
%F A376695 a(n) = A005709(n) + A005709(n-2) + A005709(n-4).
%o A376695 (PARI) a(n) = sum(k=0, n\2, binomial(n-2*k, k\3));
%o A376695 (PARI) my(N=60, x='x+O('x^N)); Vec((1+x^2+x^4)/(1-x*(1+x^6)))
%Y A376695 Cf. A000930, A098523.
%Y A376695 Cf. A005709.
%K A376695 nonn
%O A376695 0,3
%A A376695 _Seiichi Manyama_, Oct 01 2024