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A079912 Solution to the Dancing School Problem with 7 girls and n+7 boys: f(7,n). 2
1, 8, 133, 1044, 5794, 24720, 86608, 260720, 693552, 1666000, 3675680, 7549488, 14591440, 26770832, 46955760, 79197040, 129067568, 204062160, 314062912, 471875120, 693838800, 1000520848, 1417492880, 1976199792, 2714924080 (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 A079912.

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

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

FORMULA

a(0) = 1, a(1) = 8, a(2) = 133, a(3) = 1044, a(4) = 5794; for n>4, a(n) = n^7-14*n^6+126*n^5-700*n^4+2625*n^3-6342*n^2+9072*n-5840.

G.f.: -(46*x^12 -340*x^11 +931*x^10 -1808*x^9 +727*x^8 -1400*x^7 -1506*x^6 -656*x^5 -788*x^4 -148*x^3 -97*x^2 -1) / (x -1)^8. - Colin Barker, Jan 04 2015

MAPLE

seq(n^7-14*n^6+126*n^5-700*n^4+2625*n^3-6342*n^2+9072*n-5840, n=5..20);

MATHEMATICA

Join[{1, 8, 133, 1044, 5794}, Table[n^7-14n^6+126n^5-700n^4+2625n^3- 6342n^2 +9072n-5840, {n, 5, 30}]] (* Harvey P. Dale, May 03 2011 *)

PROG

(PARI) Vec(-(46*x^12 -340*x^11 +931*x^10 -1808*x^9 +727*x^8 -1400*x^7 -1506*x^6 -656*x^5 -788*x^4 -148*x^3 -97*x^2 -1) / (x -1)^8 + O(x^100)) \\ Colin Barker, Jan 04 2015

CROSSREFS

Cf. A079908-A079928.

Sequence in context: A241076 A222429 A237026 * A281948 A128287 A221545

Adjacent sequences:  A079909 A079910 A079911 * A079913 A079914 A079915

KEYWORD

nonn,easy

AUTHOR

Jaap Spies, Jan 28 2003

EXTENSIONS

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003

STATUS

approved

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Last modified March 25 12:11 EDT 2019. Contains 321470 sequences. (Running on oeis4.)