login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A079913 Solution to the Dancing School Problem with 8 girls and n+8 boys: f(8,n). 1
1, 9, 221, 2227, 15458, 80196, 334072, 1173240, 3598120, 9856552, 24553080, 56423032, 121013800, 244555560, 469343992, 860997880, 1517994792, 2583928360, 4262971000, 6839066232, 10699415080, 16362861352, 24513820920, 36042440440, 52091711272, 74112304680 (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 A079913.

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

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

FORMULA

a(0)=1, a(1)=9, a(2)=221, a(3)=2227, a(4)=15459, a(5)=80196, for n >= 6, a(n)= n^8 -20*n^7 +238*n^6 -1820*n^5 +9625*n^4 -35000*n^3 +84448*n^2 -122240*n +80680.

G.f.: -(484*x^14 -3902*x^13 +13791*x^12 -25930*x^11 +32928*x^10 -15756*x^9 +14443*x^8 +8652*x^7 +8524*x^6 +3690*x^5 +2741*x^4 +478*x^3 +176*x^2 +1) / (x -1)^9. - Colin Barker, Jan 05 2015

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9), for n>8. - Wesley Ivan Hurt, Sep 17 2015

MAPLE

A079913 := n->n^8 -20*n^7 +238*n^6 -1820*n^5 +9625*n^4 -35000*n^3 +84448*n^2 -122240*n +80680: (1, 9, 221, 2227, 15458, 80196, seq(A079913(n), n=6..30)); # edited by Wesley Ivan Hurt, Sep 17 2015

MATHEMATICA

CoefficientList[Series[-(484*x^14 - 3902*x^13 + 13791*x^12 - 25930*x^11 + 32928*x^10 - 15756*x^9 + 14443*x^8 + 8652*x^7 + 8524*x^6 + 3690*x^5 + 2741*x^4 + 478*x^3 + 176*x^2 + 1)/(x - 1)^9, {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 17 2015 *)

PROG

(PARI) Vec(-(484*x^14 -3902*x^13 +13791*x^12 -25930*x^11 +32928*x^10 -15756*x^9 +14443*x^8 +8652*x^7 +8524*x^6 +3690*x^5 +2741*x^4 +478*x^3 +176*x^2 +1)/(x -1)^9 + O(x^100)) \\ Colin Barker, Jan 05 2015

CROSSREFS

Cf. A079908-A079928.

Sequence in context: A197669 A157692 A299548 * A205578 A221439 A205568

Adjacent sequences:  A079910 A079911 A079912 * A079914 A079915 A079916

KEYWORD

nonn,easy

AUTHOR

Jaap Spies, Jan 28 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 23 18:06 EDT 2019. Contains 322387 sequences. (Running on oeis4.)