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A289121
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a(n) = (8 - 2*n + 11*n^2 - 6*n^3 + n^4)/4.
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0
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3, 4, 5, 12, 37, 98, 219, 430, 767, 1272, 1993, 2984, 4305, 6022, 8207, 10938, 14299, 18380, 23277, 29092, 35933, 43914, 53155, 63782, 75927, 89728, 105329, 122880, 142537, 164462, 188823, 215794, 245555, 278292, 314197, 353468, 396309, 442930, 493547, 548382, 607663
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OFFSET
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1,1
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COMMENTS
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For n > 1, number of maximal irredundant sets in the n-crown graph.
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LINKS
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FORMULA
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a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: x*(3 - 11*x + 15*x^2 - 3*x^3 + 2*x^4)/(1 - x)^5.
E.g.f.: (1/4)*((8 + 4*x + x^4)*exp(x) - 8). - G. C. Greubel, Aug 17 2017
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MATHEMATICA
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Table[(8 - 2 n + 11 n^2 - 6 n^3 + n^4)/4, {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {3, 4, 5, 12, 37}, 20]
CoefficientList[Series[(-3 + 11 x - 15 x^2 + 3 x^3 - 2 x^4)/(-1 + x)^5, {x, 0, 20}], x]
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PROG
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(PARI) x='x+O('x^50); Vec(x*(3 - 11*x + 15*x^2 - 3*x^3 + 2*x^4)/(1 - x)^5) \\ G. C. Greubel, Aug 17 2017
(Magma) [(8 - 2*n + 11*n^2 - 6*n^3 + n^4)/4 : n in [1..50]]; // Wesley Ivan Hurt, Dec 02 2021
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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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