A079919 Solution to the Dancing School Problem with 14 girls and n+14 boys: f(14,n).

1, 15, 4163, 158364, 3904260, 60560175, 671224467, 5697401802, 38983643908, 223245029176, 1100925116264, 4780871048064, 18612106195456, 65909241461760, 214868401724416, 650515953570304, 1842743223078144, 4916155345428736, 12422627638293760, 29881211844270336, 68721268507385344, 151698799246127104

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.

Links

Table of n, a(n) for n=0..21.

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 "dance" for computing the polynomial a(n).

Formula

a(n) = n^14 - 77*n^13 + 3094*n^12 - 83083*n^11 + 1637636*n^10 - 24785761*n^9 + 294696402*n^8 - 2779448529*n^7 + 20797459683*n^6 - 122389753486*n^5 + 555826054784*n^4 - 1883902028008*n^3 + 4494445040176*n^2 - 6742111050752*n + 4789534153984 for n >= 12. - Georg Fischer, Apr 27 2021 (polynomial computed by the program in links)

Crossrefs

Cf. A079908-A079928.

Sequence in context: A070907 A208053 A361453 * A027513 A287037 A229931

Adjacent sequences: A079916 A079917 A079918 * A079920 A079921 A079922

Keyword

nonn,easy

Author

Jaap Spies, Jan 28 2003

Extensions

Corrected by Jaap Spies, Feb 01 2004

a(13)-a(21) from Georg Fischer, Apr 27 2021

Status

approved