A079920 Solution to the Dancing School Problem with 15 girls and n+15 boys: f(15,n).

1, 16, 6746, 313464, 9479292, 174763208, 2262089361, 22088730348, 171764779170, 1106667645872, 6087616677864, 29267369636800, 125299076209408, 485013257865472, 1718947213795328, 5636819806209792, 17235204961273600, 49467590616190208, 134058587073795072, 344809293460572928, 845577589114049792, 1985060631106310400

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^15 - 90*n^14 + 4200*n^13 - 131040*n^12 + 3011190*n^11 - 53441388*n^10 + 751250500*n^9 - 8470570680*n^8 + 76896261585*n^7 - 560015385930*n^6 + 3235452199980*n^5 - 14525684311320*n^4 + 48947506506080*n^3 - 116650912956480*n^2 + 175512302620800*n - 125495209214208 for n >= 13. - Georg Fischer, Apr 27 2021 (polynomial computed by the program in links)

Crossrefs

Cf. A079908-A079928.

Sequence in context: A017008 A097547 A088654 * A203390 A221085 A280845

Adjacent sequences: A079917 A079918 A079919 * A079921 A079922 A079923

Keyword

nonn,easy

Author

Jaap Spies, Jan 28 2003

Extensions

Corrected by Jaap Spies, Feb 01 2004

a(12)-a(21) from Georg Fischer, Apr 27 2021

Status

approved