# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a079909 Showing 1-1 of 1 %I A079909 #25 Dec 03 2021 15:43:53 %S A079909 1,5,26,90,246,566,1146,2106,3590,5766,8826,12986,18486,25590,34586, %T A079909 45786,59526,76166,96090,119706,147446,179766,217146,260090,309126, %U A079909 364806,427706,498426,577590,665846,763866,872346,992006,1123590 %N A079909 Solution to the Dancing School Problem with 4 girls and n+4 boys: f(4,n). %C A079909 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. %C A079909 For fixed g, f(g,n) is polynomial in n for n >= g-2. See reference. %H A079909 Colin Barker, Table of n, a(n) for n = 0..1000 %H A079909 Jaap Spies, Dancing School Problems, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, pp. 283-285. %H A079909 Jaap Spies, Dancing School Problems, Permanent solutions of Problem 29. %H A079909 Jaap Spies, Sage program for computing A079909. %H A079909 Jaap Spies, Sage program for computing the polynomial a(n). %H A079909 Jaap Spies, A Bit of Math, The Art of Problem Solving, Jaap Spies Publishers (2019). %H A079909 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). %F A079909 a(0)=1, a(1)=5, a(n)=n^4 - 2*n^3 + 9*n^2 - 8*n + 6 (n>=2) found by applying theorem 7.2.1 of Brualdi, Ryser: Combinatorial Matrix Theory. %F A079909 G.f.: -(x^2+1)*(x^4+10*x^2+1) / (x-1)^5. - _Colin Barker_, Jan 04 2015 %F A079909 E.g.f.: exp(x)*(6 + 10*x^2 + 4*x^3 + x^4) - 5 - x. - _Stefano Spezia_, Dec 18 2019 %o A079909 (PARI) Vec(-(x^2+1)*(x^4+10*x^2+1)/(x-1)^5 + O(x^100)) \\ _Colin Barker_, Jan 04 2015 %Y A079909 Cf. A079908-A079928. %K A079909 nonn,easy %O A079909 0,2 %A A079909 _Jaap Spies_, Jan 28 2003 %E A079909 More terms from _Benoit Cloitre_, Jan 29 2003 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE