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 A079910 Solution to the Dancing School Problem with 5 girls and n+5 boys: f(5,n). 2
 1, 6, 46, 212, 738, 2104, 5150, 11196, 22162, 40688, 70254, 115300, 181346, 275112, 404638, 579404, 810450, 1110496, 1494062, 1977588, 2579554, 3320600, 4223646, 5314012, 6619538, 8170704, 10000750, 12145796, 14644962, 17540488, 20877854 (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. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Jaap Spies, Dancing School Problems, Permanent solutions of Problem 29, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, pp. 283-285. Jaap Spies, Sage program for computing A079910. 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 (6,-15,20,-15,6,-1). FORMULA a(0)=1, a(1)=6, a(2)=46, a(n) = n^5 - 5*n^4 + 25*n^3 - 55*n^2 + 80*n - 46. G.f.: (6*x^7 + 11*x^6 + 20*x^5 + 51*x^4 + 6*x^3 + 25*x^2 + 1) / (x-1)^6. - Colin Barker, Jan 04 2015 E.g.f.: 47 + 6*x + exp(x)*(-46 + 46*x + 20*x^3 + 5*x^4 + x^5). - Stefano Spezia, Dec 18 2019 MATHEMATICA CoefficientList[Series[(6 x^7 + 11 x^6 + 20 x^5 + 51 x^4 + 6 x^3 + 25 x^2 + 1) / (x - 1)^6, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 17 2015 *) PROG (PARI) Vec((6*x^7+11*x^6+20*x^5+51*x^4+6*x^3+25*x^2+1)/(x-1)^6 + O(x^100)) \\ Colin Barker, Jan 04 2015 (MAGMA) [1, 6] cat [n^5-5*n^4+25*n^3-55*n^2+80*n-46: n in [2..30]]; // Vincenzo Librandi, Feb 17 2015 CROSSREFS Cf. A079908-A079928. Sequence in context: A043076 A154651 A327935 * A103768 A325947 A240779 Adjacent sequences:  A079907 A079908 A079909 * A079911 A079912 A079913 KEYWORD nonn,easy AUTHOR Jaap Spies, Jan 28 2003 EXTENSIONS More terms from Benoit Cloitre, Jan 29 2003 STATUS approved

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Last modified May 11 21:35 EDT 2021. Contains 343808 sequences. (Running on oeis4.)