|
Search: id:A079913
|
|
|
| A079913 |
|
Solution to the Dancing School Problem with 8 girls and n+8 boys: f(8,n). |
|
+0
1
|
|
| 1, 9, 221, 2227, 15458, 80196, 334072, 1173240, 3598120, 9856552, 24553080, 56423032, 121013800, 244555560, 469343992, 860997880, 1517994792, 2583928360, 4262971000, 6839066232, 10699415080, 16362861352, 24513820920
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
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, p. 283-285.
|
|
LINKS
|
Jaap Spies, Dancing School Problems, Permanent solutions of Problem 29.
J. Spies, SAGE program for computing A079913.
J. Spies, SAGE program for computing the polynomial a(n).
|
|
FORMULA
|
a(0)=1, a(1)=9, a(2)=221, a(3)=2227, a(4)=15459, a(5)=80196, for n >= 6, a(n)= n^8-20*n^7+238*n^6-1820*n^5+9625*n^4-3500\ 0*n^3+84448*n^2-122240*n+80680.
|
|
MAPLE
|
f := n->n^8-20*n^7+238*n^6-1820*n^5+9625*n^4-35000*n^3+84448*n^2-122240*n+80680; seq(f(i), i=6..30);
|
|
CROSSREFS
|
Cf. A079908-A079928.
Adjacent sequences: A079910 A079911 A079912 this_sequence A079914 A079915 A079916
Sequence in context: A084942 A061718 A085741 this_sequence A033632 A110260 A036896
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jaap Spies (j.spies(AT)hccnet.nl), Jan 28 2003
|
|
|
Search completed in 0.002 seconds
|
