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A079921
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Solution to the Dancing School Problem with n girls and n+2 boys: f(n,2).
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1
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3, 7, 14, 26, 46, 79, 133, 221, 364, 596, 972, 1581, 2567, 4163, 6746, 10926, 17690, 28635, 46345, 75001, 121368, 196392, 317784, 514201, 832011, 1346239, 2178278, 3524546, 5702854, 9227431, 14930317, 24157781, 39088132, 63245948, 102334116, 165580101
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OFFSET
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1,1
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COMMENTS
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f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.
With offset 4, number of 132-avoiding two-stack sortable permutations which contain exactly one subsequence of type 123.
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LINKS
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FORMULA
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a(n) = a(n-1)+a(n-2)+n+1, a(1)=3, a(2)=7.
G.f.: 1/((1-x)^2*(1-x-x^2)).
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MAPLE
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with(genfunc): Fz := 1/((-1+z)^2 * (1-z-z^2)); seq(rgf_term(Fz, z, n), n=1..30);
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MATHEMATICA
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LinearRecurrence[{3, -2, -1, 1}, {3, 7, 14, 26}, 40] (* Harvey P. Dale, Oct 17 2022 *)
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CROSSREFS
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Cf. Essentially the same as A001924.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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