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A079912
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Solution to the Dancing School Problem with 7 girls and n+7: f(7,n).
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2
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1, 8, 133, 1044, 5794, 24720, 86608, 260720, 693552, 1666000, 3675680, 7549488, 14591440, 26770832, 46955760, 79197040, 129067568, 204062160, 314062912, 471875120, 693838800, 1000520848, 1417492880, 1976199792, 2714924080
(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 A079912.
J. Spies, SAGE program for computing the polynomial a(n).
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FORMULA
| a(0)=1, a(1)=8, a(2)=133, a(3)=1044, a(4)=5794; for n>4, a(n)=n^7-14*n^6+126*n^5-700*n^4+2625*n^3-6342*n^2+9072*n-5840
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MAPLE
| seq(n^7-14*n^6+126*n^5-700*n^4+2625*n^3-6342*n^2+9072*n-5840, n=5..20);
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MATHEMATICA
| Join[{1, 8, 133, 1044, 5794}, Table[n^7-14n^6+126n^5-700n^4+2625n^3- 6342n^2 +9072n-5840, {n, 5, 30}]] (* From Harvey P. Dale, May 03 2011 *)
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CROSSREFS
| Cf. A079908-A079928.
Sequence in context: A041112 A073701 A187609 * A128287 A003375 A007032
Adjacent sequences: A079909 A079910 A079911 * A079913 A079914 A079915
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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 Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003
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