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%I #18 Oct 03 2021 16:45:54
%S 1,21,465,10565,241697,5539893,127041105,2913686981,66827609633,
%T 1532754884725,35155272163473,806321934125125,18493816732267425,
%U 424174583966543669,9728877611505065297,223141752041771533125,5117984163043834408865,117386198048567829057141
%N Number of n-move queen paths on 8x8 board from given corner to any square.
%H Alois P. Heinz, <a href="/A025603/b025603.txt">Table of n, a(n) for n = 0..735</a>
%F G.f.: -(3*x-1) *(16*x^3-4*x^2-5*x+1) *(112*x^4-124*x^3-8*x^2+11*x-1) / (112896*x^9 -170880*x^8 +29184*x^7 +55636*x^6 -26128*x^5 +79*x^4 +2120*x^3 -482*x^2 +40*x-1). - _Alois P. Heinz_, Jun 26 2012
%p b:= proc(n, i, j) option remember;
%p `if`(n<0 or i<0 or i>7 or j<0 or j>7, 0, `if`(n=0,
%p 1, add(add(b(n-1, i+t*r[1], j+t*r[2]), r=[[1, 1],
%p [1, -1], [-1, 1], [-1, -1], [0, 1], [0, -1], [1, 0],
%p [-1, 0]]), t=1..7)))
%p end:
%p a:= n-> b(n, 7, 7):
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Jun 26 2012
%t b[n_, i_, j_] := b[n, i, j] = If[n<0 || i<0 || i>7 || j<0 || j>7, 0, If[n == 0, 1, Sum[Sum[b[n-1, i+t*r[[1]], j+t*r[[2]]], {r, {{1, 1}, {1, -1}, {-1, 1}, {-1, -1}, {0, 1}, {0, -1}, {1, 0}, {-1, 0}}}], {t, 1, 7}]]]; a[n_] := b[n, 7, 7]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 28 2015, after _Alois P. Heinz_ *)
%K nonn,easy
%O 0,2
%A _David W. Wilson_
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