A201508 Number of ways to place 8 nonattacking wazirs on an n X n board.

0, 0, 0, 2, 7157, 1143638, 44031035, 771464278, 8219304992, 62114308624, 364798895986, 1765597908290, 7329246973785, 26849172347850, 88645482921449, 268042562131202, 751635857876290, 1974215715426992, 4896315981217168, 11542835604897814, 26008912447737323

Offset

1,4

Comments

Wazir is a leaper [0,1].

Links

Table of n, a(n) for n=1..21.

V. Kotesovec, Non-attacking chess pieces

Formula

Explicit formula: n^16/40320 - n^14/288 + n^13/360 + 623*n^12/2880 - 41*n^11/120 - 5521*n^10/720 + 649*n^9/36 + 941767*n^8/5760 - 12485*n^7/24 - 577177*n^6/288 + 3102289*n^5/360 + 12378183*n^4/1120 - 1545219*n^3/20 + 1588751*n^2/120 + 581605*n/2 - 308806, n>=7.

G.f.: -x^4*(12*x^19 - 122*x^18 + 1130*x^17 - 6776*x^16 + 11180*x^15 + 33894*x^14 + 82772*x^13 - 1938093*x^12 + 7575029*x^11 - 10487057*x^10 - 11993287*x^9 + 70715064*x^8 - 109013258*x^7 + 41757444*x^6 + 331980470*x^5 + 173609451*x^4 + 25561181*x^3 + 1022241*x^2 + 7123*x + 2)/(x-1)^17.

a(n) = A232833(n,8). - R. J. Mathar, Apr 11 2024

Crossrefs

Cf. A172225, A172226, A172227, A172228, A178409, A201507.

Sequence in context: A129059 A129058 A129057 * A322126 A272241 A171939

Adjacent sequences: A201505 A201506 A201507 * A201509 A201510 A201511

Keyword

nonn

Author

Vaclav Kotesovec, Dec 02 2011

Status

approved