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A172211
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Number of ways to place 6 nonattacking bishops on a 6 X n board
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1
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1, 16, 313, 2320, 12160, 53744, 209428, 683524, 1905625, 4664384, 10297579, 20907590, 39664250, 71114916, 121559433, 199459466, 315906248, 485124352, 725031335, 1057839684, 1510706686, 2116429956, 2914190277, 3950340692
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history;
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OFFSET
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1,2
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n=1..32
V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes
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FORMULA
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Explicit formula (Vaclav Kotesovec, 28.1.2010): a(n) = (648n^6-17820n^5+240930n^4-2011545n^3+10806047n^2-35094560n+53430940)/10, n>=25. For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - (2k-1)/2/(k-2)!*(kn)^(k-1) + ...
G.f.: -x*(2*x^30-6*x^29+14*x^28-26*x^27+44*x^26-220*x^25+596*x^24-1060*x^23+1654*x^22
-2266*x^21+5622*x^20-13570*x^19+19848*x^18-22392*x^17+24048*x^16-30525*x^15+57673*x^14
-80154*x^13+61962*x^12-30874*x^11+25832*x^10-9360*x^9+16960*x^8-4710*x^7+18006*x^6+6928*x^5
+1968*x^4+430*x^3+222*x^2+9*x+1)/(x-1)^7 [From Vaclav Kotesovec, Mar 25 2010]
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CROSSREFS
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Cf. A061992, A172207, A172208, A172210
Sequence in context: A202878 A183886 A039746 * A053856 A208266 A184757
Adjacent sequences: A172208 A172209 A172210 * A172212 A172213 A172214
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, Jan 29 2010
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STATUS
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approved
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