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 A173965 #8 Aug 27 2025 21:10:23
%S A173965 2,9,25,56,108,187,299,450,646,893,1197,1564,2000,2511,3103,3782,4554,
%T A173965 5425,6401,7488,8692,10019,11475,13066,14798,16677,18709,20900,23256,
%U A173965 25783,28487,31374,34450,37721,41193,44872,48764,52875,57211,61778,66582,71629,76925
%N A173965 Averages of four consecutive cubes.
%H A173965 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A173965 From _R. J. Mathar_, Mar 31 2010: (Start)
%F A173965 a(n) = (2*n-1)*(n^2-n+4)/2 = (2*n-1)*A089071(n+1).
%F A173965 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A173965 G.f.: x*(1+x)*(2*x^2-x+2)/(x-1)^4. (End)
%F A173965 E.g.f.: 2 + exp(x)*(-4 + 8*x + 3*x^2 + 2*x^3)/2. - _Elmo R. Oliveira_, Aug 23 2025
%e A173965 (0^3+1^3+2^3+3^3)/4 = 9, ...
%t A173965 f[n_]:=(n^3+(n+1)^3+(n+2)^3+(n+3)^3)/4;Table[f[n],{n,-1,5!}]
%Y A173965 Cf. A027575, A089071, A173960, A173961, A173962.
%K A173965 nonn,easy,changed
%O A173965 1,1
%A A173965 _Vladimir Joseph Stephan Orlovsky_, Mar 03 2010
%E A173965 More terms from _Elmo R. Oliveira_, Aug 23 2025