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A059963 Triangle T(n,k) giving number of ways of placing n nonattacking queens on n X n board with the queen on the first row fixed at column k, 1<=k<=n.

%I A059963 #7 Mar 10 2015 01:51:38
%S A059963 1,0,0,0,0,0,0,1,1,0,2,2,2,2,2,0,1,1,1,1,0,4,7,6,6,6,7,4,4,8,16,18,18,
%T A059963 16,8,4,28,30,47,44,54,44,47,30,28,64,48,65,93,92,92,93,65,48,64,96,
%U A059963 219,209,295,346,350,346,295,209,219,96,500,806,1165,1359,1631,1639
%N A059963 Triangle T(n,k) giving number of ways of placing n nonattacking queens on n X n board with the queen on the first row fixed at column k, 1<=k<=n.
%C A059963 A000170 (non-attacking queens) can be derived from this sequence as follows: a(12)= 2*(S1(12)+S2(12)+S3(12)+S4(12)+S5(12)+S6(12)) when n is even, a(13)=S7(13) + 2*(S1(13)+S2(13)+S3(13)+S4(13)+S5(13)+S6(13)) when n is odd. Here Si(j) means T(j,i). - Patrick R. GUILLEMIN (patrick.guillemin(AT)etsi.org), Jan 05 2004
%H A059963 Patrick R. GUILLEMIN, <a href="http://agl.ifrance.com/agl/A059963.htm">Extension of triangle to 22 rows</a>
%H A059963 Patrick R. GUILLEMIN, <a href="/A059963/a059963.txt">Extension of triangle to 22 rows</a>
%e A059963 When n = 8 there are 16 ways to place if the queen on the first row is at the third column
%e A059963 Triangle begins:
%e A059963 1,
%e A059963 0,0,
%e A059963 0,0,0,
%e A059963 0,1,1,0,
%e A059963 2,2,2,2,2,
%e A059963 0,1,1,1,1,0,
%e A059963 4,7,6,6,6,7,4,
%e A059963 4,8,16,18,18,16,8,4,
%e A059963 28,30,47,44,54,44,47,30,28, etc.
%Y A059963 Cf. A000170.
%K A059963 nonn,tabl
%O A059963 1,11
%A A059963 Yong Kong (ykong(AT)curagen.com), Mar 03 2001
%E A059963 Confirmed by Patrick R. GUILLEMIN (patrick.guillemin(AT)etsi.org), who, together with colleagues, has computed the first 21 rows of this triangle, Jan 05 2004
%E A059963 Sep 15 2004: Patrick R. GUILLEMIN (patrick.guillemin(AT)etsi.org), together with colleagues, has computed the 22nd row of this triangle.