The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A054275 Susceptibility series H_2 for 2-dimensional Ising model (divided by 2). 6
 1, 8, 24, 52, 90, 140, 200, 272, 354, 448, 552, 668, 794, 932, 1080, 1240, 1410, 1592, 1784, 1988, 2202, 2428, 2664, 2912, 3170, 3440, 3720, 4012, 4314, 4628, 4952, 5288, 5634, 5992, 6360, 6740, 7130, 7532, 7944, 8368, 8802, 9248, 9704, 10172, 10650, 11140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 A. J. Guttmann, Indicators of solvability for lattice models, Discrete Math., 217 (2000), 167-189. D. Hansel et al., Analytical properties of the anisotropic cubic Ising model, J. Stat. Phys., 48 (1987), 69-80. Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA G.f.: (1+6*x+8*x^2+6*x^3+x^4) / ((1-x)^3*(1+x)). From Colin Barker, Dec 09 2016: (Start) a(n) = (11*n^2+4)/2 for n>0 and even. a(n) = (11*n^2+5)/2 for n odd. a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4. (End) E.g.f.: ((9 + 22*x + 22*x^2)*exp(x) - 4 - exp(-x))/4. - G. C. Greubel, Jul 31 2019 MATHEMATICA CoefficientList[Series[(1+6*x+8*x^2+6*x^3+x^4)/((1-x)^3*(1+x)), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 0, -2, 1}, {1, 8, 24, 52, 90}, 51] (* Indranil Ghosh, Feb 24 2017 *) Table[If[n==0, 1, (22*n^2+9-(-1)^n)/4], {n, 0, 50}] (* G. C. Greubel, Jul 31 2019 *) PROG (PARI) Vec((1+6*x+8*x^2+6*x^3+x^4)/((1-x)^3*(1+x)) + O(x^50)) \\ Colin Barker, Dec 09 2016 (PARI) a(n)=if(n, 11*n^2+5, 2)\2 \\ Charles R Greathouse IV, Feb 24 2017 (Magma) [n eq 0 select 1 else (22*n^2+9-(-1)^n)/4: n in [0..50]]; // G. C. Greubel, Jul 31 2019 (Sage) [1]+[(22*n^2+9-(-1)^n)/4 for n in (1..50)] # G. C. Greubel, Jul 31 2019 (GAP) Concatenation([1], List([1..50], n-> (22*n^2+9-(-1)^n)/4)); # G. C. Greubel, Jul 31 2019 CROSSREFS Cf. A008574, A054410, A054389, A054764. Sequence in context: A068857 A064225 A304844 * A256857 A122655 A280231 Adjacent sequences: A054272 A054273 A054274 * A054276 A054277 A054278 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, May 09 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.

Last modified November 28 17:03 EST 2023. Contains 367419 sequences. (Running on oeis4.)