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.

A109265 Row sums of Riordan array (1-x-x^2,x(1-x)).

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%I A109265 #19 Sep 08 2022 08:45:19
%S A109265 1,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,
%T A109265 2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,
%U A109265 0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0
%N A109265 Row sums of Riordan array (1-x-x^2,x(1-x)).
%H A109265 G. C. Greubel, <a href="/A109265/b109265.txt">Table of n, a(n) for n = 0..2500</a>
%H A109265 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1).
%F A109265 G.f.: (1-x-x^2)/(1-x+x^2).
%F A109265 a(n) = -a(n+3) if n>0. - _Michael Somos_, Apr 15 2015
%F A109265 a(n) = A257076(n+1). - _Michael Somos_, Apr 15 2015
%F A109265 Convolution inverse of A006355. - _Michael Somos_, Apr 15 2015
%F A109265 a(n) = A130772(n+1) = A184334(n+2) if n>0. - _Michael Somos_, Sep 01 2015
%e A109265 G.f. = 1 - 2*x^2 - 2*x^3 + 2*x^5 + 2*x^6 - 2*x^8 - 2*x^9 + 2*x^11 + 2*x^12 + ...
%t A109265 CoefficientList[Series[(1-x-x^2)/(1-x+x^2), {x, 0, 60}], x] (* _G. C. Greubel_, Aug 04 2018 *)
%t A109265 LinearRecurrence[{1,-1},{1,0,-2},120] (* _Harvey P. Dale_, Apr 08 2019 *)
%o A109265 (PARI) {a(n) = n+=2; if( n<3, n==2, 2 * (n%3>0) * (-1)^(n\3))}; /* _Michael Somos_, Apr 15 2015 */
%o A109265 (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x-x^2)/(1-x+x^2))); // _G. C. Greubel_, Aug 04 2018
%Y A109265 Cf. A006355, A109247, A130772, A184334, A257076.
%K A109265 sign,easy
%O A109265 0,3
%A A109265 _Paul Barry_, Jun 24 2005