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 A055856 Susceptibility series H_4 for 2-dimensional Ising model (divided by 2). 2
 1, 16, 90, 328, 888, 2016, 3994, 7212, 12070, 19112, 28846, 41976, 59116, 81132, 108738, 142972, 184638, 234952, 294806, 365596, 448296, 544492, 655230, 782292, 926794, 1090716, 1275238, 1482548, 1713880, 1971636, 2257102, 2572896, 2920350, 3302308, 3720138 (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 and I. G. Enting, Solvability of some statistical mechanical systems, Phys. Rev. Lett., 76 (1996), 344-347. 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 (1,3,-2,-4,0,4,2,-3,-1,1). FORMULA G.f.: (1 + 15*x + 71*x^2 + 192*x^3 + 326*x^4 + 388*x^5 + 326*x^6 + 192*x^7 + 71*x^8 + 15*x^9 + x^10)/((1-x^3)*(1-x)^4*(1+x)^3). a(n) = (4794*n^4 + 19194*n^2 + 3349 - 81*(-1)^n*(2*n^2 + 5) + 512*ChebyshevT(n, -1/2]))/1728, for n >= 1, with a(0) = 1. - G. C. Greubel, Jan 16 2020 MAPLE 1, seq( simplify( (4794*n^4 +19194*n^2 +3349 -81*(-1)^n*(2*n^2 +5) + 512*ChebyshevT(n, -1/2))/1728 ), n=1..40); # G. C. Greubel, Jan 16 2020 MATHEMATICA Join[{1}, Table[(4794*n^4 +19194*n^2 +3349 -81*(-1)^n*(2*n^2 +5) + 512*ChebyshevT[n, -1/2])/1728, {n, 40}]] (* G. C. Greubel, Jan 16 2020 *) LinearRecurrence[{1, 3, -2, -4, 0, 4, 2, -3, -1, 1}, {1, 16, 90, 328, 888, 2016, 3994, 7212, 12070, 19112, 28846}, 40] (* Harvey P. Dale, Jul 24 2021 *) PROG (PARI) Vec((1 +15*x +71*x^2 +192*x^3 +326*x^4 +388*x^5 +326*x^6 +192*x^7 + 71*x^8 +15*x^9 +x^10)/((1-x^3)*(1-x)^4*(1+x)^3) + O(x^40)) \\ Colin Barker, Dec 10 2016 (Magma) R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1 +15*x +71*x^2 +192*x^3 +326*x^4 +388*x^5 +326*x^6 +192*x^7 + 71*x^8 +15*x^9 +x^10)/((1-x^3)*(1-x^2)^3*(1-x)) )); // G. C. Greubel, Jan 16 2020 (Sage) [1]+[(4794*n^4 +19194*n^2 +3349 -81*(-1)^n*(2*n^2 +5) + 512*chebyshev_T(n, -1/2))/1728 for n in (1..40)] # G. C. Greubel, Jan 16 2020 CROSSREFS Cf. A054275, A054410, A054389, A054764, A055857. Sequence in context: A253131 A119771 A055920 * A195591 A240292 A050406 Adjacent sequences: A055853 A055854 A055855 * A055857 A055858 A055859 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Jun 07 2000 STATUS approved

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Last modified May 30 03:22 EDT 2024. Contains 372957 sequences. (Running on oeis4.)