Search: id:a054410
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A054410
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Susceptibility series H_3 for 2-dimensional Ising model (divided by 2).
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+0
6
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1, 12, 52, 148, 328, 620, 1052, 1652, 2448, 3468, 4740, 6292, 8152, 10348, 12908, 15860, 19232, 23052, 27348, 32148, 37480, 43372, 49852, 56948, 64688, 73100, 82212, 92052, 102648, 114028, 126220, 139252, 153152, 167948, 183668, 200340, 217992, 236652
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1 +8*x +10*x^2 +8*x^3 +x^4)/(1-x)^4.
a(n) = 2*n*(11 + 7*n^2)/3 for n>0.
a(0)=1, a(1)=12, a(2)=52, a(3)=148, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4. (End)
E.g.f.: (3 + 2*x*(18 + 21*x + 7*x^2)*exp(x))/3. - G. C. Greubel, Jul 31 2019
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MATHEMATICA
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CoefficientList[Series[(1+8*x+10*x^2+8*x^3+x^4)/(1-x)^4, {x, 0, 40}], x] (* or *) a[0]=1; a[n_]:= 2*n*(11+7*n^2)/3; Table[a[n], {n, 0, 40}] (* Indranil Ghosh, Feb 24 2017 *)
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PROG
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(PARI) Vec((1+8*x+10*x^2+8*x^3+x^4)/(1-x)^4 + O(x^40)) \\ Colin Barker, Dec 09 2016
(PARI) vector(40, n, n--; if(n==0, 1, 2*n*(11+7*n^2)/3)) \\ G. C. Greubel, Jul 31 2019
(Python)
if n == 0: return 1
(Magma) [1] cat [2*n*(11+7*n^2)/3: n in [1..40]]; // G. C. Greubel, Jul 31 2019
(Sage) [1]+[2*n*(11+7*n^2)/3 for n in (1..40)] # G. C. Greubel, Jul 31 2019
(GAP) Concatenation([1], List([1..40], n-> 2*n*(11+7*n^2)/3)); # G. C. Greubel, Jul 31 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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