A172215 Number of ways to place 6 nonattacking knights on a 6 X n board.

1, 58, 729, 8830, 60285, 257318, 858262, 2404448, 5879329, 12927182, 26115008, 49238436, 87675623, 148787822, 242366502, 381127124, 581249573, 862965246, 1251190796, 1776208532, 2474393475, 3388987070, 4570917554, 6079666980

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

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Formula

a(n) = (648n^6-11340n^5+103770n^4-606645n^3+2328317n^2-5466660n+6051720)/10, n>=10.

G.f.: -x * (104*x^15 -116*x^14 -1328*x^13 +3992*x^12 +806*x^11 -16380*x^10 +27343*x^9 -4845*x^8 -15537*x^7 +38275*x^6 -2753*x^5 +11789*x^4 +4910*x^3 +344*x^2 +51*x +1) / (x-1)^7. - Vaclav Kotesovec, Mar 25 2010

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Wesley Ivan Hurt, Apr 16 2023

Mathematica

CoefficientList[Series[-(104 x^15 - 116 x^14 - 1328 x^13 + 3992 x^12 + 806 x^11 - 16380 x^10 + 27343 x^9 - 4845 x^8 - 15537 x^7 + 38275 x^6 - 2753 x^5 + 11789 x^4 + 4910 x^3 + 344 x^2 + 51 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 58, 729, 8830, 60285, 257318, 858262, 2404448, 5879329, 12927182, 26115008, 49238436, 87675623, 148787822, 242366502, 381127124}, 30] (* Harvey P. Dale, Dec 31 2022 *)

Crossrefs

Cf. A061992, A172212, A172213, A172214.

Sequence in context: A246894 A204470 A254954 * A305263 A157252 A142966

Adjacent sequences: A172212 A172213 A172214 * A172216 A172217 A172218

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Status

approved