A172232 -id:A172232 - cp's OEIS frontend

A172234 Number of ways to place 7 nonattacking wazirs on a 7 X n board.

0, 2, 1478, 50726, 573797, 3581924, 15516804, 52550366, 149162199, 370817854, 831571604, 1717417198, 3316210152, 6054985120, 10545491888, 17638773534, 28489610297, 44631652698, 68064067456, 101350519742, 147731315314, 211249526076, 296891922604, 410745537182

Offset: 1

Vaclav Kotesovec, Jan 29 2010

Wazir is a (fairy chess) leaper [0,1].

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)

Cf. A172229, A172230, A172231, A172232, A061993.

CoefficientList[Series[x (7 x^11 - 48 x^10 + 370 x^9 + 40 x^8 + 8541 x^7 + 45282 x^6 + 190420 x^5 + 329248 x^4 + 209261 x^3 + 38958 x^2 + 1462 x+2) / (x - 1)^8, {x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)

a(n) = (117649*n^7-1663893*n^6+10942729*n^5-43685355*n^4+114945646*n^3-199980312*n^2+213228096*n-107390880)/720, n>=6.
For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - (k-1)(5k-2)/2/k!*(kn)^(k-1) + ...
G.f.: x^2*(7*x^11-48*x^10+370*x^9+40*x^8+8541*x^7+45282*x^6+190420*x^5 +329248*x^4+209261*x^3+38958*x^2+1462*x+2)/(x-1)^8. - Vaclav Kotesovec, Mar 25 2010

More terms from Vincenzo Librandi, May 29 2013

A178410 Number of ways to place 8 nonattacking wazirs on an 8 X n board.

Original entry on oeis.org

0, 2, 4374, 259289, 4255370, 35093344, 189681689, 771464278, 2559099153, 7285273805, 18416621598, 42342480425, 90097012004, 179755977430, 339666241815, 612682858064, 1061605357051, 1776021648675, 2880784715492

Offset: 1

Vaclav Kotesovec, May 27 2010

Wazir is a (fairy chess) leaper [0,1].

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
V. Kotesovec, Non-attacking chess pieces, 6ed, 2013

Cf. A172229, A172230, A172231, A172232, A172234.

CoefficientList[Series[- x (8 x^13 - 112 x^12 + 870 x^11 - 2812 x^10 + 15019 x^9 + 41114 x^8 + 494109 x^7 + 2357839 x^6 + 5805509 x^5 + 5762254 x^4 + 2079065 x^3 + 219995 x^2 + 4356 x + 2) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)

a(n) = (1048576*n^8 -17432576*n^7 +136349696*n^6 -658958720*n^5 +2161896569*n^4 -4945969574*n^3 +7719028159*n^2 -7516702410*n +3494080800) / 2520, n >= 7.

G.f.: -x^2 * (8*x^13 -112*x^12 +870*x^11 -2812*x^10 +15019*x^9 +41114*x^8 +494109*x^7 +2357839*x^6 +5805509*x^5 +5762254*x^4 +2079065*x^3 +219995*x^2 +4356*x +2) / (x-1)^9.

cp's OEIS Frontend

A172234 Number of ways to place 7 nonattacking wazirs on a 7 X n board.

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