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 A019561 #21 Nov 21 2021 12:05:43
%S A019561 1,50,450,1970,5890,14002,28610,52530,89090,142130,216002,315570,
%T A019561 446210,613810,824770,1086002,1404930,1789490,2248130,2789810,3424002,
%U A019561 4160690,5010370,5984050,7093250,8350002
%N A019561 Coordination sequence for C_5 lattice.
%H A019561 Seiichi Manyama, <a href="/A019561/b019561.txt">Table of n, a(n) for n = 0..10000</a>
%H A019561 M. Baake and U. Grimm, <a href="https://arxiv.org/abs/cond-mat/9706122">Coordination sequences for root lattices and related graphs</a>, arXiv:cond-mat/9706122, Zeit. f. Kristallographie, 212 (1997), 253-256.
%H A019561 R. Bacher, P. de la Harpe and B. Venkov, <a href="http://dx.doi.org/10.1016/S0764-4442(97)83542-2">Séries de croissance et séries d'Ehrhart associées aux réseaux de racines</a>, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
%H A019561 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A019561 G.f.: (1+45*x+210*x^2+210*x^3+45*x^4+x^5)/(1-x)^5 = 1+2*x*(5+10*x+x^2)^2/(1-x)^5.
%F A019561 G.f. for sequence with interpolated zeros: cosh(10*arctanh(x)) = 1/2*( ((1 + x)/(1 - x))^5 + ((1 - x)/(1 + x))^5 ) = 1 + 50*x^2 + 450*x^4 + 1970*x^6 + .... - _Peter Bala_, Apr 09 2017
%F A019561 a(n) = A008413(2*n). - _Seiichi Manyama_, Jun 08 2018
%t A019561 LinearRecurrence[{5,-10,10,-5,1},{1,50,450,1970,5890,14002},30] (* _Harvey P. Dale_, Nov 21 2021 *)
%Y A019561 Cf. A103884 (row 5). For coordination sequences of other C_n lattices see A022144 (C_2), A010006 (C3), A019560 - A019564 (C_4 through C_8), A035746 - A035787 (C_9 through C_50).
%Y A019561 Cf. A008413, A137513.
%K A019561 nonn,easy
%O A019561 0,2
%A A019561 mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)