A172229 Number of ways to place 3 nonattacking wazirs on a 3 X n board.

0, 2, 22, 84, 215, 442, 792, 1292, 1969, 2850, 3962, 5332, 6987, 8954, 11260, 13932, 16997, 20482, 24414, 28820, 33727, 39162, 45152, 51724, 58905, 66722, 75202, 84372, 94259, 104890, 116292, 128492, 141517, 155394, 170150, 185812, 202407, 219962, 238504

Offset: 1

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

• nonn
• easy

Comments

A 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
• R. J. Mathar, Bivariate generating functions for non-attacking wazirs on rectangular boards, viXra:2404.0122 (2024) Section 3.
• Eric Weisstein's World of Mathematics, Grid Graph
• Wikipedia, Wazir (chess)

Crossrefs

Cf. A172226, A061989.

Column w=3 of A371967.

Programs

Mathematica

CoefficientList[Series[x (3 x^3 + 8 x^2 + 14 x + 2) / (x - 1)^4, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Formula

a(n) = (3*n - 5)*(3*n^2 - 8*n + 8)/2, n>=2.

G.f.: x^2*(3*x^3+8*x^2+14*x+2)/(x-1)^4. - Vaclav Kotesovec, Mar 25 2010