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A079915 Solution to the Dancing School Problem with 10 girls and n+10 boys: f(10,n). 1
1, 11, 596, 9627, 103129, 780902, 4557284, 21670160, 87396728, 308055528, 971055240, 2780440664, 7324967640, 17945144328, 41249101928, 89635336440, 185317652664, 366517590440, 696695849928 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

REFERENCES

Jaap Spies, Dancing School Problems, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, pp. 283-285.

LINKS

Table of n, a(n) for n=0..18.

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).

FORMULA

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.

MAPLE

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 +21623220*n^2 -31840760*n +21750840: seq(f(i), i=8..21);

CROSSREFS

Cf. A079908-A079928.

Sequence in context: A263184 A288326 A260583 * A185656 A142738 A262015

Adjacent sequences:  A079912 A079913 A079914 * A079916 A079917 A079918

KEYWORD

nonn

AUTHOR

Jaap Spies, Jan 28 2003

EXTENSIONS

Corrected by Jaap Spies, Feb 01 2004

STATUS

approved

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Last modified April 21 10:03 EDT 2019. Contains 322328 sequences. (Running on oeis4.)