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A079911 Solution to the Dancing School Problem with 6 girls and n+6 boys: f(6,n). 2
1, 7, 79, 478, 2108, 7364, 21652, 55532, 127604, 268108, 523244, 960212, 1672972, 2788724, 4475108, 6948124, 10480772, 15412412, 22158844, 31223108, 43207004, 58823332, 78908852, 104437964, 136537108, 176499884, 225802892, 286122292 (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 A079911.

J. Spies, Sage program for computing the polynomial a(n).

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

a(0)=1, a(2)=7, a(3)=79, a(n)=n^6-9*n^5+60*n^4-225*n^3+555*n^3-774*n+484.

G.f.: -(6*x^10 -29*x^9 +120*x^8 -49*x^7 +267*x^6 +105*x^5 +211*x^4 +37*x^3 +51*x^2 +1) / (x -1)^7. - Colin Barker, Jan 04 2015

MAPLE

seq(n^6-9*n^5+60*n^4-225*n^3+555*n^2-774*n+484, n=4..40);

PROG

(PARI) Vec(-(6*x^10 -29*x^9 +120*x^8 -49*x^7 +267*x^6 +105*x^5 +211*x^4 +37*x^3 +51*x^2 +1) / (x -1)^7 + O(x^100)) \\ Colin Barker, Jan 04 2015

CROSSREFS

Cf. A079908-A079928.

Sequence in context: A154592 A075896 A201475 * A003545 A104094 A220382

Adjacent sequences:  A079908 A079909 A079910 * A079912 A079913 A079914

KEYWORD

nonn,easy

AUTHOR

Jaap Spies, Jan 28 2003

STATUS

approved

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Last modified March 21 20:16 EDT 2019. Contains 321382 sequences. (Running on oeis4.)