The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A055920 Susceptibility series H_4 for 2-dimensional Ising model (divided by 2) for 1 particle excitation. 2
1, 16, 90, 328, 886, 2016, 3986, 7208, 12050, 19096, 28802, 41936, 59030, 81048, 108586, 142816, 184386, 234688, 294410, 365176, 447702, 543856, 654370, 781368, 925586, 1089416, 1273586, 1480768, 1711670, 1969256, 2254202, 2569776, 2916610, 3298288, 3715386 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
A. J. Guttmann, Indicators of solvability for lattice models, Discrete Math., 217 (2000), 167-189 (H_4(1)/2 of Section 3).
FORMULA
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).
From Colin Barker, Dec 10 2016: (Start)
a(n) = (133*n^4 + 524*n^2 + 96)/48 for n>0 and even.
a(n) = (133*n^4 + 542*n^2 + 93)/48 for n odd.
(End)
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
1/2 of column 4 of A055921.
Sequence in context: A192129 A253131 A119771 * A055856 A195591 A240292
KEYWORD
nonn,easy
AUTHOR
Christian G. Bower, Jun 19 2000
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 28 15:56 EDT 2024. Contains 372916 sequences. (Running on oeis4.)