A172232 Number of ways to place 6 nonattacking wazirs on a 6 X n board.

0, 2, 504, 10010, 78052, 368868, 1280832, 3612344, 8774380, 19049692, 37898664, 70311824, 123209012, 205885204, 330502992, 512631720, 771833276, 1132294540, 1623506488, 2280989952, 3147068036, 4271685188, 5713272928, 7539662232, 9829042572, 12670967612

Offset

1,2

Comments

Wazir is a (fairy chess) leaper [0,1].

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

Eric Weisstein's World of Mathematics, Grid Graph

Wikipedia, Wazir (chess)

Formula

a(n) = 2*(486*n^6 -5670*n^5 +30240*n^4 -95230*n^3 +187899*n^2 -220775*n +120540) / 15, n>=5.

G.f.: -2*x^2 * (3*x^9 -5*x^8 +100*x^7 +354*x^6 +2548*x^5 +7572*x^4 +9248*x^3 +3262*x^2 +245*x +1) / (x-1)^7. - Vaclav Kotesovec, Mar 25 2010

Mathematica

CoefficientList[Series[- 2 x (3 x^9 - 5 x^8 + 100 x^7 + 354 x^6 + 2548 x^5 + 7572 x^4 + 9248 x^3 + 3262 x^2 + 245 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Crossrefs

Cf. A172229, A172230, A172231, A061992.

Sequence in context: A322759 A178468 A024032 * A253706 A109032 A362539

Adjacent sequences: A172229 A172230 A172231 * A172233 A172234 A172235

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Status

approved