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 A131878 #24 Mar 31 2025 18:34:46
%S A131878 1,22,57,106,169,246,337,442,561,694,841,1002,1177,1366,1569,1786,
%T A131878 2017,2262,2521,2794,3081,3382,3697,4026,4369,4726,5097,5482,5881,
%U A131878 6294,6721,7162,7617,8086,8569,9066,9577,10102,10641,11194,11761,12342,12937,13546,14169,14806,15457,16122,16801,17494
%N A131878 a(n) = 7*n^2 + 14*n + 1.
%C A131878 The original terms listed here were incorrect: 1002 through 8086 were listed as 988 through 8072, consistently 14 lower than the actual values. - _Russ Cox_, Apr 18 2024
%H A131878 Harvey P. Dale, <a href="/A131878/b131878.txt">Table of n, a(n) for n = 0..1000</a>
%H A131878 Takao Komatsu, Ritika Goel, and Neha Gupta, <a href="https://arxiv.org/abs/2409.14788">The Frobenius number for the triple of the 2-step star numbers</a>, arXiv:2409.14788 [math.CO], 2024. See p. 2.
%H A131878 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A131878 Binomial transform of (1, 21, 14, 0, 0, 0, ...).
%F A131878 a(n) = a(n-1) + 14*n + 7 (with a(0)=1). - _Vincenzo Librandi_, Nov 23 2010
%F A131878 Row sums of triangle A131876.
%F A131878 From _Stefano Spezia_, Sep 27 2024: (Start)
%F A131878 G.f.: (1 + 19*x - 6*x^2)/(1 - x)^3.
%F A131878 E.g.f.: exp(x)*(1 + 21*x + 7*x^2). (End)
%e A131878 a(2) = 57 = sum of row 2 terms of triangle A131876: (29 + 15 + 13).
%e A131878 a(2) = 57 = (1, 2, 1) dot (1, 21, 14) = (1 + 42 + 14).
%t A131878 Table[7n^2+14n+1,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,22,57},50] (* _Harvey P. Dale_, Mar 31 2025 *)
%Y A131878 Cf. A131876.
%K A131878 nonn,easy
%O A131878 0,2
%A A131878 _Gary W. Adamson_, Jul 22 2007
%E A131878 Corrected and extended by _Russ Cox_, Apr 18 2024