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A079909
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Solution to the Dancing School Problem with 4 girls and n+4 boys: f(4,n).
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2
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1, 5, 26, 90, 246, 566, 1146, 2106, 3590, 5766, 8826, 12986, 18486, 25590, 34586, 45786, 59526, 76166, 96090, 119706, 147446, 179766, 217146, 260090, 309126, 364806, 427706, 498426, 577590, 665846, 763866, 872346, 992006, 1123590
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.
For fixed g, f(g,n) is polynomial in n for n >= g-2. See reference.
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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.
J. Spies, SAGE program for computing A079909.
J. Spies, SAGE program for computing the polynomial a(n).
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FORMULA
| a(0)=1, a(1)=5, a(n)=n^4 - 2*n^3 + 9*n^2 - 8*n + 6 (n>=2) found by applying theorem 7.2.1 of Brualdi, Ryser: Combinatorial Matrix Theory.
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CROSSREFS
| Cf. A079908-A079928.
Sequence in context: A145013 A096943 A166810 * A047669 A002316 A005499
Adjacent sequences: A079906 A079907 A079908 * A079910 A079911 A079912
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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 from Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 29 2003
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