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 A256716 #32 Aug 04 2025 14:21:13
%S A256716 0,1,25,94,230,455,791,1260,1884,2685,3685,4906,6370,8099,10115,12440,
%T A256716 15096,18105,21489,25270,29470,34111,39215,44804,50900,57525,64701,
%U A256716 72450,80794,89755,99355,109616,120560,132209,144585,157710,171606,186295,201799,218140
%N A256716 a(n) = n*(n+1)*(22*n-19)/6.
%C A256716 This sequence is related to the tridecagonal numbers (A051865) by a(n) = n*A051865(n) - Sum_{i=0..n-1} A051865(i).
%D A256716 E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (22nd row of the table).
%H A256716 Bruno Berselli, <a href="/A256716/b256716.txt">Table of n, a(n) for n = 0..1000</a>
%H A256716 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A256716 G.f.: x*(1 + 21*x)/(1 - x)^4.
%F A256716 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with n>3, a(0)=0, a(1)=1, a(2)=25, a(3)=94.
%F A256716 a(n) = Sum_{i=0..n-1} (n-i)*(22*i+1) for n>0.
%F A256716 E.g.f.: exp(x)*x*(6 + 69*x + 22*x^2)/6. - _Elmo R. Oliveira_, Aug 04 2025
%t A256716 Table[n (n + 1) (22 n - 19)/6, {n, 0, 40}]
%o A256716 (PARI) vector(40, n, n--; n*(n+1)*(22*n-19)/6)
%o A256716 (Sage) [n*(n+1)*(22*n-19)/6 for n in (0..40)]
%o A256716 (Magma) [n*(n+1)*(22*n-19)/6: n in [0..40]];
%Y A256716 Partial sums of A051876.
%Y A256716 Cf. similar sequences listed in A237616.
%Y A256716 Cf. A051865.
%K A256716 nonn,easy
%O A256716 0,3
%A A256716 _Bruno Berselli_, Apr 09 2015