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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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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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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REFERENCES
| Jaap Spies, Dancing School Problems, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, p. 283-285.
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LINKS
| Jaap Spies, Dancing School Problems, Permanent solutions of Problem 29.
E. S. Egge and T. Mansour, 132-avoiding two-stack sortable permutations....
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FORMULA
| 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))
F(n+5) - n - 4, F(n) = A000045(n).
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MAPLE
| 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
| CoefficientList[Series[(-z^3 + z^2 + 2*z - 3)/((z - 1)^2 (z^2 + z - 1)), {z, 0, 100}], z] (* From Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)
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CROSSREFS
| Cf. A079908-A079928, A001924.
Cf. Essentially the same as A001924.
Sequence in context: A036830 A014153 A001924 * A014168 A132109 A099854
Adjacent sequences: A079918 A079919 A079920 * A079922 A079923 A079924
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KEYWORD
| nonn
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AUTHOR
| Jaap Spies (j.spies(AT)hccnet.nl), Jan 28 2003
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EXTENSIONS
| More terms Dec 15 2006
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