cp's OEIS Frontend

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.

A357178 First differences of cubes of triangular numbers.

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%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