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%I #25 Dec 03 2021 15:43:53
%S 1,5,26,90,246,566,1146,2106,3590,5766,8826,12986,18486,25590,34586,
%T 45786,59526,76166,96090,119706,147446,179766,217146,260090,309126,
%U 364806,427706,498426,577590,665846,763866,872346,992006,1123590
%N Solution to the Dancing School Problem with 4 girls and n+4 boys: f(4,n).
%C 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 For fixed g, f(g,n) is polynomial in n for n >= g-2. See reference.
%H Colin Barker, <a href="/A079909/b079909.txt">Table of n, a(n) for n = 0..1000</a>
%H Jaap Spies, <a href="http://www.nieuwarchief.nl/serie5/pdf/naw5-2006-07-4-283.pdf">Dancing School Problems</a>, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, pp. 283-285.
%H Jaap Spies, <a href="http://www.jaapspies.nl/mathfiles/dancingschool.pdf">Dancing School Problems, Permanent solutions of Problem 29</a>.
%H Jaap Spies, <a href="http://www.jaapspies.nl/oeis/a079909.sage">Sage program for computing A079909</a>.
%H Jaap Spies, <a href="http://www.jaapspies.nl/mathfiles/dancing.sage">Sage program for computing the polynomial a(n)</a>.
%H Jaap Spies, <a href="http://www.jaapspies.nl/bookb5.pdf">A Bit of Math, The Art of Problem Solving</a>, Jaap Spies Publishers (2019).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F 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 G.f.: -(x^2+1)*(x^4+10*x^2+1) / (x-1)^5. - _Colin Barker_, Jan 04 2015
%F E.g.f.: exp(x)*(6 + 10*x^2 + 4*x^3 + x^4) - 5 - x. - _Stefano Spezia_, Dec 18 2019
%o (PARI) Vec(-(x^2+1)*(x^4+10*x^2+1)/(x-1)^5 + O(x^100)) \\ _Colin Barker_, Jan 04 2015
%Y Cf. A079908-A079928.
%K nonn,easy
%O 0,2
%A _Jaap Spies_, Jan 28 2003
%E More terms from _Benoit Cloitre_, Jan 29 2003
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