login
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.
1
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, 16, 8, 4, 28, 30, 47, 44, 54, 44, 47, 30, 28, 64, 48, 65, 93, 92, 92, 93, 65, 48, 64, 96, 219, 209, 295, 346, 350, 346, 295, 209, 219, 96, 500, 806, 1165, 1359, 1631, 1639
OFFSET
1,11
COMMENTS
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
EXAMPLE
When n = 8 there are 16 ways to place if the queen on the first row is at the third column
Triangle begins:
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,
4,8,16,18,18,16,8,4,
28,30,47,44,54,44,47,30,28, etc.
CROSSREFS
Cf. A000170.
Sequence in context: A037868 A173069 A363934 * A137934 A133738 A240713
KEYWORD
nonn,tabl
AUTHOR
Yong Kong (ykong(AT)curagen.com), Mar 03 2001
EXTENSIONS
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
Sep 15 2004: Patrick R. GUILLEMIN (patrick.guillemin(AT)etsi.org), together with colleagues, has computed the 22nd row of this triangle.
STATUS
approved