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 A131877 #20 Apr 03 2024 15:15:59 %S A131877 1,15,29,43,57,71,85,99,113,127,141,155,169,183,197,211,225,239,253, %T A131877 267,281,295,309,323,337,351,365,379,393,407,421,435,449,463,477,491, %U A131877 505,519,533,547,561,575,589,603,617,631,645,659,673,687,701,715,729 %N A131877 a(n) = 14*n + 1. %C A131877 Left column of triangle A131876. %C A131877 Binomial transform of (1, 14, 0, 0, 0, ...). %C A131877 Partial sums give A051868. - _Leo Tavares_, Mar 19 2023 %H A131877 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1). %F A131877 a(n) = 14*n + 1. %F A131877 From _Elmo R. Oliveira_, Apr 03 2024: (Start) %F A131877 G.f.: (1+13*x)/(1-x)^2. %F A131877 E.g.f.: exp(x)*(1 + 14*x). %F A131877 a(n) = A051868(n+1) - A051868(n). %F A131877 a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End) %e A131877 a(2) = 29 = 2*14 + 1. %e A131877 a(2) = 29 = (1, 2, 1) dot (1, 14, 0) = (1 + 28 + 0). %t A131877 Range[1, 1000, 14] (* _Vladimir Joseph Stephan Orlovsky_, May 31 2011 *) %Y A131877 Cf. A008596, A131876. %Y A131877 Cf. A051868. %K A131877 nonn %O A131877 0,2 %A A131877 _Gary W. Adamson_, Jul 22 2007