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.

A126264 a(n) = 5*n^2 + 3*n.

This page as a plain text file.
%I A126264 #25 Aug 21 2022 04:19:44
%S A126264 8,26,54,92,140,198,266,344,432,530,638,756,884,1022,1170,1328,1496,
%T A126264 1674,1862,2060,2268,2486,2714,2952,3200,3458,3726,4004,4292,4590,
%U A126264 4898,5216,5544,5882,6230,6588,6956,7334,7722,8120,8528,8946,9374,9812,10260
%N A126264 a(n) = 5*n^2 + 3*n.
%D A126264 L. B. W. Jolley, Summation of Series, Dover Publications, 1961, p. 12
%H A126264 G. C. Greubel, <a href="/A126264/b126264.txt">Table of n, a(n) for n = 1..5000</a>
%H A126264 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A126264 Sum_{i=1..n} a(i) = n*(n+1)*(5n+7)/3 = 2*A162148(n).
%F A126264 a(n) = 2*A147875(n+1).
%F A126264 From _G. C. Greubel_, Aug 23 2017: (Start)
%F A126264 G.f.: 2*x*(x + 4)/(1 - x)^3.
%F A126264 E.g.f.: x*(5*x + 8)*exp(x). (End)
%F A126264 Sum_{n>=1} 1/a(n) = 5/9 + sqrt(1-2/sqrt(5))*Pi/6 + log(phi)*sqrt(5)/6 - 5*log(5)/12, where phi is the golden ratio (A001622). - _Amiram Eldar_, Aug 21 2022
%e A126264 a(24) = 5*24^2 + 3*24 = 2880 + 72 = 2952.
%p A126264 a:=n->5*n^2+3*n: seq(a(n),n=1..55); # _Emeric Deutsch_, Apr 17 2007
%t A126264 Table[n*(5*n + 3), {n,1,50}] (* _G. C. Greubel_, Aug 23 2017 *)
%o A126264 (PARI) a(n)=5*n^2+3*n \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A126264 Cf. A001622, A147875.
%K A126264 nonn,easy
%O A126264 1,1
%A A126264 _Gary W. Adamson_, Dec 22 2006
%E A126264 More terms from _Emeric Deutsch_, Apr 17 2007