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Search: id:A079915
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| A079915 |
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Solution to the Dancing School Problem with 10 girls and n+10 boys: f(10,n). |
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1
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| 1, 11, 596, 9627, 103129, 780902, 4557284, 21670160, 87396728, 308055528, 971055240, 2780440664, 7324967640, 17945144328, 41249101928, 89635336440, 185317652664, 366517590440, 696695849928
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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.
For fixed g, f(g,n) is polynomial in n for n >= g-2. See reference.
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REFERENCES
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Jaap Spies, Dancing School Problems, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, p. 283-285.
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LINKS
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Jaap Spies, Dancing School Problems, Permanent solutions of Problem 29.
J. Spies, SAGE program for computing A079915.
J. Spies, SAGE program for computing the polynomial a(n).
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FORMULA
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for n>=8 a(n)=n^10-35*n^9+675*n^8-8610*n^7+78435*n^6-523467*n^5+2562525*n^4-9008160*n^3+21623220*n^2-31840760*n+21750840
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MAPLE
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f := n->n^10-35*n^9+675*n^8-8610*n^7+78435*n^6-523467*n^5+2562525*n^4-9008160*n^3+216\ 23220*n^2-31840760*n+21750840 seq(f(i), i=8..21);
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CROSSREFS
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Cf. A079908-A079928.
Adjacent sequences: A079912 A079913 A079914 this_sequence A079916 A079917 A079918
Sequence in context: A004800 A065823 A049654 this_sequence A142738 A115737 A036933
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KEYWORD
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nonn
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AUTHOR
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Jaap Spies (j.spies(AT)hccnet.nl), Jan 28 2003
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EXTENSIONS
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Corrected by Jaap Spies (j.spies(AT)hccnet.nl), Feb 01 2004
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