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 A357178 #54 Sep 01 2025 19:00:37 %S A357178 0,1,26,189,784,2375,5886,12691,24704,44469,75250,121121,187056, %T A357178 279019,404054,570375,787456,1066121,1418634,1858789,2402000,3065391, %U A357178 3867886,4830299,5975424,7328125,8915426,10766601,12913264,15389459,18231750,21479311,25174016,29360529 %N A357178 First differences of cubes of triangular numbers. %C A357178 Row sums of centered hexagonal numbers A003215 treated as a regular triangle. %H A357178 Kelvin Voskuijl, <a href="/A357178/b357178.txt">Table of n, a(n) for n = 0..10000</a> %H A357178 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1). %F A357178 a(n) = (n^3 + 3*n^5)/4. %F A357178 G.f.: x*(1 + 20*x + 48*x^2 + 20*x^3 + x^4)/(1 - x)^6. - _Stefano Spezia_, Sep 19 2022 %t A357178 a[n_] := (n^3 + 3*n^5)/4; Array[a, 35, 0] (* _Amiram Eldar_, Sep 18 2022 *) %o A357178 (PARI) a(n) = n^3*(3*n^2+1)/4 \\ _Charles R Greathouse IV_, Sep 19 2022 %Y A357178 Cf. A059827 (cubes of triangular numbers). %Y A357178 Cf. A000578 (for squares) and A168364 (for fourth powers) of triangular numbers. %Y A357178 Cf. A000217 (triangular numbers), A003215. %K A357178 nonn,easy,changed %O A357178 0,3 %A A357178 _Kelvin Voskuijl_, Sep 16 2022