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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A079914 Solution to the Dancing School Problem with 9 girls and n+9 boys: f(9,n). 1
1, 10, 364, 4664, 40296, 253072, 1249768, 5112544, 17990600, 56010096, 157175032, 403579328, 959942664, 2136701200, 4488418616, 8961185952, 17105944648, 31378295984, 55549351800, 95256535936, 158727963272, 257719103568 (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 A079914.

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

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

FORMULA

a(0)=1, a(1)=10, a(2)=364, a(3)=4664, a(4)=40296, a(5)=253072, a(6)=1249768, for n >= 7: a(n)=n^9-27n^8+414n^7-4158n^6+29421n^5-148743n^4+530796n^3-1276992n^2+1866384n-1255608.

G.f.: -(5840*x^16 -52960*x^15 +210480*x^14 -481464*x^13 +671100*x^12 -619882*x^11 +258311*x^10 -123144*x^9 -98197*x^8 -57276*x^7 -46818*x^6 -18160*x^5 -9046*x^4 -1354*x^3 -309*x^2 -1) / (x -1)^10.- Colin Barker, Jan 05 2015

MAPLE

f := n->n^9-27*n^8+414*n^7-4158*n^6+29421*n^5-148743*n^4+530796*n^3-1276992*n^2+1866384*n-1255608; seq(f(i), i=7..21);

PROG

(PARI) Vec(-(5840*x^16 -52960*x^15 +210480*x^14 -481464*x^13 +671100*x^12 -619882*x^11 +258311*x^10 -123144*x^9 -98197*x^8 -57276*x^7 -46818*x^6 -18160*x^5 -9046*x^4 -1354*x^3 -309*x^2 -1) / (x -1)^10 + O(x^100)) \\ Colin Barker, Jan 05 2015

CROSSREFS

Cf. A079908-A079928.

Sequence in context: A301310 A247335 A112694 * A051790 A220638 A119547

Adjacent sequences:  A079911 A079912 A079913 * A079915 A079916 A079917

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.)