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A059963
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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.
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1
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,11
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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
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LINKS
| Patrick R. GUILLEMIN, Extension of triangle to 22 rows
Patrick R. GUILLEMIN, Extension of triangle to 22 rows
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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.
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CROSSREFS
| Cf. A000170.
Sequence in context: A037869 A037868 A173069 * A137934 A133738 A111409
Adjacent sequences: A059960 A059961 A059962 * A059964 A059965 A059966
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KEYWORD
| nonn,tabl
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AUTHOR
| Yong Kong (ykong(AT)curagen.com), Mar 03 2001
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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 22-nd row of this triangle.
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