A172210 Number of ways to place 5 nonattacking bishops on a 5 X n board.
1, 12, 143, 770, 3368, 12632, 38566, 98968, 222351, 450682, 843169, 1479116, 2460912, 3917228, 6006056, 8917888, 12878847, 18153806, 25049515, 33917724, 45158308, 59222392, 76615476, 97900560, 123701269, 154704978, 191665937, 235408396, 286829730, 346903564
Offset: 1
Links
- 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
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Programs
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Mathematica
CoefficientList[Series[(2 x^20 - 4 x^19 + 8 x^18 - 12 x^17 - 48 x^16 + 140 x^15 - 158 x^14 + 208 x^13 + 134 x^12 - 932 x^11 + 1048*x^10 -182*x^9+ 436 * x^8 + 396 x^7 - 32 x^6 + 1288 * x^5 + 668 * x^4 + 72 * x^3 + 86 * x^2 + 6 * x + 1) / (x - 1)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)
Formula
a(n) = (625n^5-11250n^4+98875n^3-515250n^2+1566016n-2194944)/24, n>=16.
G.f.: x*(2*x^20 -4*x^19 +8*x^18 -12*x^17 -48*x^16 +140*x^15 -158*x^14 +208*x^13 +134*x^12 -932*x^11 +1048*x^10 -182*x^9 +436*x^8 +396*x^7 -32*x^6 +1288*x^5 +668*x^4 +72*x^3 +86*x^2 +6*x+1)/(x-1)^6. - Vaclav Kotesovec, Mar 25 2010