A172211 Number of ways to place 6 nonattacking bishops on a 6 X n board.

1, 16, 313, 2320, 12160, 53744, 209428, 683524, 1905625, 4664384, 10297579, 20907590, 39664250, 71114916, 121559433, 199459466, 315906248, 485124352, 725031335, 1057839684, 1510706686, 2116429956, 2914190277, 3950340692

Offset

1,2

Links

Vaclav Kotesovec and Vincenzo Librandi, Table of n, a(n) for n = 1..1000 (first 32 terms from V. Kotesovec)

V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

Formula

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. - Vaclav Kotesovec, Mar 25 2010

Mathematica

CoefficientList[Series[-(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, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)

Crossrefs

Cf. A061992, A172207, A172208, A172210.

Sequence in context: A232834 A232841 A320064 * A254151 A053856 A208266

Adjacent sequences: A172208 A172209 A172210 * A172212 A172213 A172214

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Status

approved