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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.

Jaap Spies, Sage program for computing A079911.

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

Jaap Spies, A Bit of Math, The Art of Problem Solving, Jaap Spies Publishers (2019).

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);

MATHEMATICA

CoefficientList[Series[-(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, {x, 0, 28}], x] (* Michael De Vlieger, Dec 23 2019 *)

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 July 11 03:56 EDT 2020. Contains 335609 sequences. (Running on oeis4.)