A172230 Number of ways to place 4 nonattacking wazirs on a 4 X n board.

0, 2, 61, 405, 1502, 4072, 9091, 17791, 31660, 52442, 82137, 123001, 177546, 248540, 339007, 452227, 591736, 761326, 965045, 1207197, 1492342, 1825296, 2211131, 2655175, 3163012, 3740482, 4393681, 5128961, 5952930, 6872452, 7894647

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) = (64*n^4 - 432*n^3 + 1235*n^2 - 1797*n + 1122)/6, n>=3.

G.f.: -x^2*(4*x^5+12*x^4+67*x^3+120*x^2+51*x+2)/(x-1)^5. - Vaclav Kotesovec, Mar 25 2010

Mathematica

CoefficientList[Series[- x (4 x^5 + 12 x^4 + 67 x^3 + 120 x^2 + 51 x + 2) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Crossrefs

Cf. A172227, A172229, A061990.

Sequence in context: A167215 A279624 A088078 * A059004 A297919 A298543

Adjacent sequences: A172227 A172228 A172229 * A172231 A172232 A172233

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Extensions

More terms from Vincenzo Librandi, May 28 2013

Status

approved