A201508 - OEIS

%I #11 Apr 11 2024 14:01:07

%S 0,0,0,2,7157,1143638,44031035,771464278,8219304992,62114308624,

%T 364798895986,1765597908290,7329246973785,26849172347850,

%U 88645482921449,268042562131202,751635857876290,1974215715426992,4896315981217168,11542835604897814,26008912447737323

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

%C Wazir is a leaper [0,1].

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>

%F 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.

%F 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.

%F a(n) = A232833(n,8). - _R. J. Mathar_, Apr 11 2024

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

%K nonn

%O 1,4

%A _Vaclav Kotesovec_, Dec 02 2011