A055920 - OEIS

%I #11 Aug 16 2021 13:59:13

%S 1,16,90,328,886,2016,3986,7208,12050,19096,28802,41936,59030,81048,

%T 108586,142816,184386,234688,294410,365176,447702,543856,654370,

%U 781368,925586,1089416,1273586,1480768,1711670,1969256,2254202,2569776,2916610,3298288,3715386

%N Susceptibility series H_4 for 2-dimensional Ising model (divided by 2) for 1 particle excitation.

%H Colin Barker, <a href="/A055920/b055920.txt">Table of n, a(n) for n = 0..1000</a>

%H A. J. Guttmann, <a href="https://doi.org/10.1016/S0012-365X(99)00262-9">Indicators of solvability for lattice models</a>, Discrete Math., 217 (2000), 167-189 (H_4(1)/2 of Section 3).

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).

%F G.f.: (1 +14*x +56*x^2 +122*x^3 +146*x^4 +122*x^5 +56*x^6 +14*x^7 +x^8) / ((1 -x)^5*(1 +x)^3).

%F From _Colin Barker_, Dec 10 2016: (Start)

%F a(n) = (133*n^4 + 524*n^2 + 96)/48 for n>0 and even.

%F a(n) = (133*n^4 + 542*n^2 + 93)/48 for n odd.

%F (End)

%t LinearRecurrence[{2,2,-6,0,6,-2,-2,1},{1,16,90,328,886,2016,3986,7208,12050},40] (* _Harvey P. Dale_, Oct 08 2017 *)

%o (PARI) Vec((1 +14*x +56*x^2 +122*x^3 +146*x^4 +122*x^5 +56*x^6 +14*x^7 +x^8)/((1 -x)^5*(1 +x)^3) + O(x^50)) \\ _Colin Barker_, Dec 10 2016

%Y 1/2 of column 4 of A055921.

%K nonn,easy

%O 0,2

%A _Christian G. Bower_, Jun 19 2000