A201507 Number of ways to place 7 nonattacking wazirs on an n X n board.

0, 0, 0, 20, 12798, 763144, 15516804, 170842828, 1264750240, 7084450248, 32251861624, 125030824732, 426265242412, 1308045124808, 3675893768908, 9586626461484, 23445303141400, 54219244028296, 119372323892736, 251614892723068, 510130577706724, 998740710435208

Offset

1,4

Comments

Wazir is a leaper [0,1].

Links

Table of n, a(n) for n=1..22.

V. Kotesovec, Non-attacking chess pieces

Formula

Explicit formula: n^14/5040 - n^12/48 + n^11/60 + 137*n^10/144 - 3*n^9/2 - 1139*n^8/48 + 223*n^7/4 + 59293*n^6/180 - 3191*n^5/3 - 8719*n^4/4 + 51737*n^3/5 + 10914*n^2/7 - 40708*n + 37228, n>=6.

G.f.: 2*x^4*(5*x^16 - 31*x^15 + 193*x^14 - 1683*x^13 + 5093*x^12 + 12431*x^11 - 111239*x^10 + 214181*x^9 + 187845*x^8 - 1518841*x^7 + 2546483*x^6 - 775465*x^5 - 6212549*x^4 - 2702167*x^3 - 286637*x^2 - 6249*x - 10)/(x-1)^15.

a(n) = A232833(n,7). - R. J. Mathar, Apr 11 2024

Crossrefs

Cf. A172225, A172226, A172227, A172228, A178409.

Sequence in context: A086687 A173790 A028667 * A167060 A172661 A172758

Adjacent sequences: A201504 A201505 A201506 * A201508 A201509 A201510

Keyword

nonn

Author

Vaclav Kotesovec, Dec 02 2011

Status

approved