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 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 J. Spies, Sage program for computing A079914. 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

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