login
A174698
Number of ways to place 8 nonattacking knights on an 8 X n board.
1
1, 81, 4409, 175720, 2479881, 17925691, 92952858, 379978716, 1286959255, 3765248749, 9805497200, 23226916560, 50866495373, 104288896551, 202154535834, 373400685738, 661407061211, 1129334088897, 1866838857216
OFFSET
1,2
FORMULA
Explicit formula: a(n) = (262144*n^8 -6881280*n^7+93456384*n^6 -838693632*n^5 +5361604836*n^4 -24739168020*n^3+79766188151*n^2 -163079018193*n +160750559340)/630, n>=14.
G.f.: x*(592*x^21 -584*x^20 -18100*x^19 +49628*x^18+134264*x^17 -735838*x^16 +584418*x^15+2607764*x^14 -7093608*x^13 +5656936*x^12 +5136811*x^11 -13973779*x^10 +14583702*x^9 -1612610*x^8 +2009820*x^7 +6682287*x^6 +1572406*x^5 +1050447*x^4 +138871*x^3+3716*x^2 +72*x+1)/(1-x)^9.
MATHEMATICA
CoefficientList[Series[(592 x^21 - 584 x^20 - 18100 x^19 + 49628 x^18 + 134264 x^17 - 735838 x^16 + 584418 x^15 + 2607764 x^14 - 7093608 x^13 + 5656936 x^12 + 5136811 x^11 - 13973779 x^10 + 14583702 x^9 - 1612610 x^8 + 2009820 x^7 + 6682287 x^6 + 1572406 x^5 + 1050447 x^4 + 138871 x^3 + 3716 x^2 + 72 x + 1) / (1 - x)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 30 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Mar 27 2010
STATUS
approved