A172217 Number of ways to place 7 nonattacking knights on a 7 X n board.

1, 78, 1758, 38588, 383246, 2135344, 8891854, 30108310, 86669806, 219845764, 504261973, 1065642840, 2104251027, 3924818982, 6973786593, 11884673662, 19532410762, 31097451768, 48140491605, 72688612756, 107333684073

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = (117649n^7-2571471n^6+29223943n^5-216954465n^4+1114503256n^3-3907492824n^2+8562799512n-8962924320)/720,n>=12.

For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - 3(k-1)(3k-4)/2/k!*(kn)^(k-1) + ...

G.f.: x * (252*x^18 -272*x^17 -5134*x^16 +14468*x^15 +19721*x^14 -132666*x^13 +174233*x^12 +119440*x^11 -540473*x^10 +654954*x^9 -89133*x^8 -93778*x^7 +497782*x^6 +56796*x^5 +119468*x^4 +26652*x^3 +1162*x^2 +70*x +1) / (x-1)^8. - Vaclav Kotesovec, Mar 25 2010

Mathematica

CoefficientList[Series[(252 x^18 - 272 x^17 - 5134 x^16 + 14468 x^15 + 19721 x^14 - 132666 x^13 + 174233 x^12 + 119440 x^11 - 540473 x^10 + 654954 x^9 - 89133 x^8 - 93778 x^7 + 497782 x^6 + 56796 x^5 + 119468 x^4 + 26652 x^3 + 1162 x^2 + 70 x + 1) / (x - 1)^8, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)

Crossrefs

Cf. A061993, A172212, A172213, A172214, A172215.

Sequence in context: A264362 A160839 A187590 * A036524 A262063 A140934

Adjacent sequences: A172214 A172215 A172216 * A172218 A172219 A172220

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Status

approved