A079914 Solution to the Dancing School Problem with 9 girls and n+9 boys: f(9,n).
1, 10, 364, 4664, 40296, 253072, 1249768, 5112544, 17990600, 56010096, 157175032, 403579328, 959942664, 2136701200, 4488418616, 8961185952, 17105944648, 31378295984, 55549351800, 95256535936, 158727963272, 257719103568
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Jaap Spies, Dancing School Problems, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, pp. 283-285.
- Jaap Spies, Dancing School Problems, Permanent solutions of Problem 29.
- Jaap Spies, Sage program for computing A079914.
- 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 (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
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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);
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Mathematica
CoefficientList[Series[-(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, {x, 0, 21}], x] (* Michael De Vlieger, Dec 23 2019 *) -
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
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
Comments