This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A366971 #18 Oct 31 2023 00:52:04 %S A366971 0,0,1,5,15,36,71,131,216,346,511,756,1042,1441,1907,2527,3207,4128, %T A366971 5097,6371,7737,9442,11213,13538,15848,18734,21744,25423,29077,33743, %U A366971 38238,43818,49440,56104,62694,70979,78749,88154,97580,108790,119450,132680,145021,159974 %N A366971 a(n) = Sum_{k=3..n} binomial(k,3) * floor(n/k). %F A366971 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 A366971 a(n) = (A064603(n) - 3*A064602(n) + 2*A024916(n))/6. - _Chai Wah Wu_, Oct 30 2023 %o A366971 (PARI) a(n) = sum(k=3, n, binomial(k, 3)*(n\k)); %o A366971 (Python) %o A366971 from math import isqrt, comb %o A366971 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 A366971 Partial sums of A363607. %Y A366971 Cf. A366968, A366969, A366970. %Y A366971 Cf. A024916, A064602, A064603, A366967. %K A366971 nonn %O A366971 1,4 %A A366971 _Seiichi Manyama_, Oct 30 2023