|
Search: id:A079914
|
|
|
| A079914 |
|
Solution to the Dancing School Problem with 9 girls and n+9 boys: f(9,n). |
|
+0
1
|
|
| 1, 10, 364, 4664, 40296, 253072, 1249768, 5112544, 17990600, 56010096, 157175032, 403579328, 959942664, 2136701200, 4488418616, 8961185952, 17105944648, 31378295984, 55549351800, 95256535936, 158727963272, 257719103568
(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 A079914.
J. Spies, SAGE program for computing the polynomial a(n).
|
|
FORMULA
|
a(0)=1, a(1)=10, a(2)=364, a(3)=4664, a(4)=40296, a(5)=253072, a(6)=1249768, for n >= 7: a(n)=n^9-27n^8+414n^7-4158n^6+29421n^5-148743n^4+530796n^3-1276992n^2+1866384n-1255608
|
|
MAPLE
|
f := n->n^9-27*n^8+414*n^7-4158*n^6+29421*n^5-148743*n^4+530796*n^3-1276992*n^2+18663\ 84*n-1255608; seq(f(i), i=7..21);
|
|
CROSSREFS
|
Cf. A079908-A079928.
Sequence in context: A132093 A016101 A112694 this_sequence A051790 A119547 A117797
Adjacent sequences: A079911 A079912 A079913 this_sequence A079915 A079916 A079917
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jaap Spies (j.spies(AT)hccnet.nl), Jan 28 2003
|
|
|
Search completed in 0.002 seconds
|
