|
| |
|
|
A079909
|
|
Solution to the Dancing School Problem with 4 girls and n+4 boys: f(4,n).
|
|
3
|
|
|
|
1, 5, 26, 90, 246, 566, 1146, 2106, 3590, 5766, 8826, 12986, 18486, 25590, 34586, 45786, 59526, 76166, 96090, 119706, 147446, 179766, 217146, 260090, 309126, 364806, 427706, 498426, 577590, 665846, 763866, 872346, 992006, 1123590
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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.
|
|
|
REFERENCES
|
Jaap Spies, Dancing School Problems, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, pp. 283-285.
|
|
|
LINKS
|
Colin Barker, Table of n, a(n) for n = 0..1000
Jaap Spies, Dancing School Problems, Permanent solutions of Problem 29.
J. Spies, Sage program for computing A079909.
J. Spies, Sage program for computing the polynomial a(n).
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
|
|
|
FORMULA
|
a(0)=1, a(1)=5, a(n)=n^4 - 2*n^3 + 9*n^2 - 8*n + 6 (n>=2) found by applying theorem 7.2.1 of Brualdi, Ryser: Combinatorial Matrix Theory.
G.f.: -(x^2+1)*(x^4+10*x^2+1) / (x-1)^5. - Colin Barker, Jan 04 2015
|
|
|
PROG
|
(PARI) Vec(-(x^2+1)*(x^4+10*x^2+1)/(x-1)^5 + O(x^100)) \\ Colin Barker, Jan 04 2015
|
|
|
CROSSREFS
|
Cf. A079908-A079928.
Sequence in context: A166810 A210367 A261347 * A047669 A002316 A211606
Adjacent sequences: A079906 A079907 A079908 * A079910 A079911 A079912
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Jaap Spies, Jan 28 2003
|
|
|
EXTENSIONS
|
More terms from Benoit Cloitre, Jan 29 2003
|
|
|
STATUS
|
approved
|
| |
|
|
