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A348621
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The number of additions required to compute the permanent of general n X n matrices using Ryser's formula without Gray code ordering.
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0
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0, 4, 21, 82, 275, 836, 2373, 6406, 16647, 41992, 103433, 249866, 593931, 1392652, 3227661, 7405582, 16842767, 38010896, 85196817, 189792274, 420478995, 926941204, 2034237461, 4445962262, 9680453655, 21005074456, 45432700953, 97978941466, 210721832987, 452045307932
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OFFSET
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1,2
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REFERENCES
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Herbert John Ryser, Combinatorial Mathematics, volume 14 of Carus Mathematical Monographs. American Mathematical Soc., (1963), pp. 24-28.
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LINKS
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FORMULA
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a(n) = (n^2 - 2*n + 2)*2^(n-1) + n - 2.
a(n) = 8*a(n-1) - 25*a(n-2) + 38*a(n-3) - 28*a(n-4) + 8*a(n-5) for n > 5.
O.g.f.: x^2*(4 - 11*x + 14*x^2 - 8*x^3)/((1 - x)^2*(1 - 2*x)^3).
E.g.f.: 1 + exp(x)*(x - 2) + exp(2*x)*(2*x^2 - x + 1).
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MATHEMATICA
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LinearRecurrence[{8, -25, 38, -28, 8}, {0, 4, 21, 82, 275}, 30]
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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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