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%I #18 Oct 31 2023 00:52:04
%S 0,0,1,5,15,36,71,131,216,346,511,756,1042,1441,1907,2527,3207,4128,
%T 5097,6371,7737,9442,11213,13538,15848,18734,21744,25423,29077,33743,
%U 38238,43818,49440,56104,62694,70979,78749,88154,97580,108790,119450,132680,145021,159974
%N a(n) = Sum_{k=3..n} binomial(k,3) * floor(n/k).
%F G.f.: 1/(1-x) * Sum_{k>=1} x^(3*k)/(1-x^k)^4 = 1/(1-x) * Sum_{k>=3} binomial(k,3) * x^k/(1-x^k).
%F a(n) = (A064603(n) - 3*A064602(n) + 2*A024916(n))/6. - _Chai Wah Wu_, Oct 30 2023
%o (PARI) a(n) = sum(k=3, n, binomial(k, 3)*(n\k));
%o (Python)
%o from math import isqrt, comb
%o def A366971(n): return -comb((s:=isqrt(n))+1,4)*(s+1)+sum(comb((q:=n//w)+1,4)+(q+1)*comb(w,3) for w in range(1,s+1)) # _Chai Wah Wu_, Oct 30 2023
%Y Partial sums of A363607.
%Y Cf. A366968, A366969, A366970.
%Y Cf. A024916, A064602, A064603, A366967.
%K nonn
%O 1,4
%A _Seiichi Manyama_, Oct 30 2023
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