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.

A131056 A007318 * A131055.

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%I A131056 #22 Apr 30 2022 18:00:22
%S A131056 1,3,7,17,41,97,225,513,1153,2561,5633,12289,26625,57345,122881,
%T A131056 262145,557057,1179649,2490369,5242881,11010049,23068673,48234497,
%U A131056 100663297,209715201,436207617,905969665
%N A131056 A007318 * A131055.
%H A131056 Harvey P. Dale, <a href="/A131056/b131056.txt">Table of n, a(n) for n = 1..1000</a>
%H A131056 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4)
%F A131056 Binomial transform of A131055: (1, 2, 2, 4, 4, 6, 6, ...). A131056 = A131054 as an infinite lower triangular matrix * [1,2,3,...] as a vector.
%F A131056 G.f.: x*(1-2*x+2*x^3)/((1-x)*(1-2*x)^2); a(n)=-0^n/2+2^(n-1)*(n+1)+1. - _Paul Barry_, Jun 14 2008
%F A131056 a(n) = 2+A099035(n-1), n>1. - _Juri-Stepan Gerasimov_, Oct 02 2011
%e A131056 a(4) = 17 = (1, 3, 3, 1) dot (1, 2, 2, 4) = (1 + 6 + 6 + 4).
%t A131056 LinearRecurrence[{5,-8,4},{1,3,7,17},40] (* _Harvey P. Dale_, Apr 30 2022 *)
%o A131056 (PARI) Vec(x*(1-2*x+2*x^3)/((1-x)*(1-2*x)^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 12 2015
%Y A131056 Cf. A131055, A131054, A141222.
%K A131056 nonn,easy
%O A131056 1,2
%A A131056 _Gary W. Adamson_, Jun 12 2007
%E A131056 More terms from _Paul Barry_, Jun 14 2008