A079915 Solution to the Dancing School Problem with 10 girls and n+10 boys: f(10,n).

1, 11, 596, 9627, 103129, 780902, 4557284, 21670160, 87396728, 308055528, 971055240, 2780440664, 7324967640, 17945144328, 41249101928, 89635336440, 185317652664, 366517590440, 696695849928

Offset: 0

Author

Jaap Spies, Jan 28 2003

Keywords

• nonn

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

• Jaap Spies, Dancing School Problems, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, pp. 283-285.
• Jaap Spies, Dancing School Problems, Permanent solutions of Problem 29.
• Jaap Spies, Sage program for computing A079915.
• Jaap Spies, Sage program for computing the polynomial a(n).
• Jaap Spies, A Bit of Math, The Art of Problem Solving, Jaap Spies Publishers (2019).

Crossrefs

Cf. A079908-A079928.

Programs

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 [phone]*n^2 -31840760*n [phone]: seq(f(i), i=8..21);

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 [phone]*n^2 -31840760*n [phone].

Extensions

Corrected by Jaap Spies, Feb 01 2004