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.

A264754 Expansion of (1 + 2*x - 2*x^3 + x^4)/((1 - x)^3*(1 + x)^2).

This page as a plain text file.
%I A264754 #36 Sep 10 2016 10:36:14
%S A264754 1,3,5,7,11,13,19,21,29,31,41,43,55,57,71,73,89,91,109,111,131,133,
%T A264754 155,157,181,183,209,211,239,241,271,273,305,307,341,343,379,381,419,
%U A264754 421,461,463,505,507,551,553,599,601,649,651,701,703,755,757,811,813,869,871,929,931,991,993,1055,1057,1121,1123
%N A264754 Expansion of (1 + 2*x - 2*x^3 + x^4)/((1 - x)^3*(1 + x)^2).
%C A264754 Interleaving of A002061 and A028387.
%C A264754 All members are odd.
%C A264754 Primes in this sequence: 3, 5, 7, 11, 13, 19, 29, 31, 41, 43, 71, 73, 89, 109, 131, 157, 181, 211, 239, 241, 271, 307, 379, 419, 421, 461, 463, 599, 601, 701, 757, 811, 929, 991, ...
%H A264754 Carauleanu Marc, <a href="/A264754/b264754.txt">Table of n, a(n) for n = 0..2222</a>
%H A264754 Ilya Gutkovskiy, <a href="/A264754/a264754.pdf">Illustration</a>
%H A264754 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A264754 O.g.f.: (1 + 2*x - 2*x^3 + x^4)/((1 - x)^3*(1 + x)^2).
%F A264754 E.g.f.: ((-3 - 2*x)*exp(-x) + (11 + 12*x + 2*x^2)*exp(x))/8
%F A264754 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 4.
%F A264754 a(n) = (2*n*(n + (-1)^n + 5) - 3*(-1)^n + 11)/8.
%t A264754 LinearRecurrence[{1, 2, -2, -1, 1}, {1, 3, 5, 7, 11}, 66]
%t A264754 Table[(2 n (n + (-1)^n + 5) - 3 (-1)^n + 11)/8, {n, 0, 65}]
%o A264754 (PARI) Vec((1+2*x-2*x^3+x^4)/((1-x)^3*(1+x)^2) + O(x^99)) \\ _Altug Alkan_, Aug 27 2016
%Y A264754 Cf. A002061, A005408, A028387, A055802.
%K A264754 nonn,easy
%O A264754 0,2
%A A264754 _Ilya Gutkovskiy_, Aug 27 2016