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%I #24 Jul 02 2022 11:39:46
%S 1,7,79,478,2108,7364,21652,55532,127604,268108,523244,960212,1672972,
%T 2788724,4475108,6948124,10480772,15412412,22158844,31223108,43207004,
%U 58823332,78908852,104437964,136537108,176499884,225802892,286122292
%N Solution to the Dancing School Problem with 6 girls and n+6 boys: f(6,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="/A079911/b079911.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/a079911.sage">Sage program for computing A079911</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_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(0)=1, a(2)=7, a(3)=79, a(n)=n^6-9*n^5+60*n^4-225*n^3+555*n^3-774*n+484.
%F G.f.: -(6*x^10 -29*x^9 +120*x^8 -49*x^7 +267*x^6 +105*x^5 +211*x^4 +37*x^3 +51*x^2 +1) / (x -1)^7. - _Colin Barker_, Jan 04 2015
%p seq(n^6-9*n^5+60*n^4-225*n^3+555*n^2-774*n+484,n=4..40);
%t CoefficientList[Series[-(6 x^10 - 29 x^9 + 120 x^8 - 49 x^7 + 267 x^6 + 105 x^5 + 211 x^4 + 37 x^3 + 51 x^2 + 1)/(x - 1)^7, {x, 0, 28}], x] (* _Michael De Vlieger_, Dec 23 2019 *)
%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,7,79,478,2108,7364,21652,55532,127604,268108,523244},40] (* _Harvey P. Dale_, Jul 02 2022 *)
%o (PARI) Vec(-(6*x^10 -29*x^9 +120*x^8 -49*x^7 +267*x^6 +105*x^5 +211*x^4 +37*x^3 +51*x^2 +1) / (x -1)^7 + O(x^100)) \\ _Colin Barker_, Jan 04 2015
%Y Cf. A079908-A079928.
%K nonn,easy
%O 0,2
%A _Jaap Spies_, Jan 28 2003
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