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%I #13 May 12 2023 14:59:56
%S 0,0,0,784,40496,451104,2803552,12139552,41792672,121269248,310362944,
%T 718151344,1534460624,3067048224,5801302304,10464095808,18125622336,
%U 30299632896,49104515712,77410664016,119081302128,179178580768
%N Number of 7-turn bishop's tours on an n X n board summed over all starting positions.
%C Row 7 of A188777.
%H R. H. Hardin, <a href="/A188782/b188782.txt">Table of n, a(n) for n = 1..28</a>
%F Contribution from _Vaclav Kotesovec_, Sep 01 2012: (Start)
%F Empirical: Recurrence: a(n) = a(n-14) - 4*a(n-13) + a(n-12) + 16*a(n-11) - 19*a(n-10) - 20*a(n-9) + 45*a(n-8) - 45*a(n-6) + 20*a(n-5) + 19*a(n-4) - 16*a(n-3) - a(n-2) + 4*a(n-1).
%F Empirical: G.f.: 16*x^4*(49 + 2335*x + 18119*x^2 + 65761*x^3 + 125593*x^4 + 154411*x^5 + 109333*x^6 + 52763*x^7 + 12090*x^8 + 1722*x^9)/((1-x)^9*(1+x)^5).
%F Empirical: a(n) = 6421/16 - 581677*n/210 + 2022619*n^2/315 - 340262*n^3/45 + 1915471*n^4/360 - 106466*n^5/45 + 29363*n^6/45 - 31916*n^7/315 + 16943*n^8/2520 + (-1)^n*(-6421/16 + 1645*n/2 - 557*n^2 + 155*n^3 - 123*n^4/8).
%F (End)
%e Some solutions for 4 X 4
%e ..0..4..0..2....0..3..0..0....4..0..0..0....0..0..1..0....0..0..3..0
%e ..7..0..3..0....4..0..2..0....0..3..0..7....0..5..0..2....0..1..0..4
%e ..0..1..0..5....0..6..0..1....2..0..6..0....4..0..6..0....2..0..6..0
%e ..0..0..6..0....7..0..5..0....0..1..0..5....0..3..0..7....0..5..0..7
%Y Cf. A188777.
%K nonn
%O 1,4
%A _R. H. Hardin_, Apr 10 2011
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