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%I #10 Oct 17 2024 08:22:52
%S 1,0,0,2,2,0,3,12,3,4,36,36,9,80,180,86,155,600,607,402,1581,2808,
%T 1967,3780,9816,10376,10584,28626,44918,41184,77627,160436,181044,
%U 228972,499512,735654,811823,1467072,2640231,3191642,4494502,8566308,12280547,15315974,26498718
%N a(n) = Sum_{k=0..floor(n/3)} (k+1) * binomial(k,n-3*k)^2.
%F G.f.: (1-x^3-x^4)/((1-x^3-x^4)^2 - 4*x^7)^(3/2).
%o (PARI) a(n) = sum(k=0, n\3, (k+1)*binomial(k, n-3*k)^2);
%Y Cf. A182884, A375218.
%Y Cf. A376721.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Oct 17 2024