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 A187307 #22 Feb 19 2025 12:11:04
%S A187307 1,2,2,-1,-5,-5,1,8,8,-1,-11,-11,1,14,14,-1,-17,-17,1,20,20,-1,-23,
%T A187307 -23,1,26,26,-1,-29,-29,1,32,32,-1,-35,-35,1,38,38,-1,-41,-41,1,44,44,
%U A187307 -1,-47,-47,1,50,50,-1,-53,-53,1,56,56,-1,-59,-59,1
%N A187307 Hankel transform of an alternating sum of Motzkin numbers.
%C A187307 Hankel transform of A187306.
%H A187307 Michael De Vlieger, <a href="/A187307/b187307.txt">Table of n, a(n) for n = 0..9999</a>
%H A187307 Paul Barry, <a href="https://arxiv.org/abs/2004.04577">On a Central Transform of Integer Sequences</a>, arXiv:2004.04577 [math.CO], 2020.
%H A187307 Paul Barry, <a href="https://doi.org/10.3390/math13020242">Extensions of Riordan Arrays and Their Applications</a>, Mathematics (2025) Vol. 13, No. 2, 242. See p. 16.
%H A187307 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-3,2,-1)
%F A187307 G.f.: (1+x^2-x^3)/(1-x+x^2)^2.
%F A187307 a(n) = (1/3)*(2*n+2-(n-1)*cos(2*n*Pi/3)-(n-1)*cos(4*n*Pi/3)-cos((2*n+1)*Pi/3)-sin((8*n+1)*Pi/6))*(-1)^floor(n/3). - _Wesley Ivan Hurt_, Sep 25 2017
%t A187307 LinearRecurrence[{2,-3,2,-1},{1,2,2,-1},120] (* _Harvey P. Dale_, Jan 21 2019 *)
%o A187307 (PARI) Vec((1+x^2-x^3)/(1-x+x^2)^2 + O(x^80)) \\ _Michel Marcus_, Sep 26 2017
%Y A187307 Cf. A187306.
%K A187307 sign,easy
%O A187307 0,2
%A A187307 _Paul Barry_, Mar 08 2011