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 A264892 #21 Feb 16 2025 08:33:27
%S A264892 0,1,176,1281,4720,12545,27456,52801,92576,151425,234640,348161,
%T A264892 498576,693121,939680,1246785,1623616,2080001,2626416,3273985,4034480,
%U A264892 4920321,5944576,7120961,8463840,9988225,11709776,13644801,15810256,18223745,20903520
%N A264892 a(n) = n*(3*n - 2)*(9*n^2 - 6*n - 2).
%C A264892 Doubly octagonal numbers.
%H A264892 G. C. Greubel, <a href="/A264892/b264892.txt">Table of n, a(n) for n = 0..5000</a>
%H A264892 OEIS Wiki, <a href="https://oeis.org/wiki/Figurate_numbers">Figurate numbers</a>
%H A264892 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>
%H A264892 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1)
%F A264892 G.f.: x*(1 + 171*x + 411*x^2 + 65*x^3)/(1 - x)^5.
%F A264892 a(n) = A000567(A000567(n)).
%F A264892 Sum_{n>0} 1/a(n) = (sqrt(3)*gamma + sqrt(3)*polygamma(0, 1/3) - polygamma(0, (1/3)*(2 - sqrt(3))) + polygamma(0, (1/3)*(2 + sqrt(3))))/(4*sqrt(3)) = 1.006842786293...,where gamma is the Euler-Mascheroni constant (A001620), and polygamma is the derivative of the logarithm of the gamma function.
%t A264892 Table[n (3 n - 2) (9 n^2 - 6 n - 2), {n, 0, 30}]
%o A264892 (PARI) concat(0, Vec(x*(1+171*x+411*x^2+65*x^3)/(1-x)^5 + O(x^100))) \\ _Altug Alkan_, Nov 27 2015
%o A264892 (Magma) [n*(3*n-2)*(9*n^2-6*n-2): n in [0..30]]; // _Vincenzo Librandi_, Nov 28 2015
%Y A264892 Cf. A000567, A002817, A000583, A232713, A063249.
%K A264892 nonn,easy
%O A264892 0,3
%A A264892 _Ilya Gutkovskiy_, Nov 27 2015