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 A363978 #10 Jun 30 2023 15:35:35 %S A363978 0,0,1,0,0,1,3,0,1,0,6,1,0,3,11,0,0,1,15,0,4,6,21,1,0,0,29,3,0,11,36, %T A363978 0,7,0,48,1,0,15,56,0,0,4,66,6,11,21,78,1,3,0,92,0,0,29,111,3,16,0, %U A363978 120,11,0,36,140,0,0,7,153,0,22,48,171,1,0,0,201,15,9,56,210,0,29,0,231,4,0,66,254,6,0 %N A363978 Expansion of Sum_{k>0} x^(3*k) / (1 - x^(4*k))^3. %F A363978 G.f.: Sum_{k>0} k*(k+1)/2 * x^(4*k-1) / (1 - x^(4*k-1)). %F A363978 a(n) = Sum_{d|n, d==3 mod 4} binomial((d+1)/4+1,2). %t A363978 a[n_] := DivisorSum[n, Binomial[(#+1)/4+1,2] &, Mod[#, 4] == 3 &]; Array[a, 100] (* _Amiram Eldar_, Jun 30 2023 *) %o A363978 (PARI) a(n) = sumdiv(n, d, (d%4==3)*binomial((d+1)/4+1, 2)); %Y A363978 Cf. A363973. %K A363978 nonn %O A363978 1,7 %A A363978 _Seiichi Manyama_, Jun 30 2023