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A172213
Number of ways to place 4 nonattacking knights on a 4 X n board.
6
1, 16, 84, 412, 1416, 3640, 7928, 15384, 27352, 45432, 71480, 107608, 156184, 219832, 301432, 404120, 531288, 686584, 873912, 1097432, 1361560, 1670968, 2030584, 2445592, 2921432
OFFSET
1,2
FORMULA
Explicit formula (Vaclav Kotesovec, 26.1.2010): a(n) = 8*(4n^4-36n^3+170n^2-450n+537)/3, n>=6
G.f.: -x*(16*x^9-20*x^8-40*x^7+172*x^6-81*x^5+41*x^4+142*x^3+14*x^2+11*x+1)/(x-1)^5 [From Vaclav Kotesovec, Mar 25 2010]
MATHEMATICA
CoefficientList[Series[-(16 x^9 - 20 x^8 - 40 x^7 + 172 x^6 - 81 x^5 + 41 x^4 + 142 x^3 + 14 x^2 + 11 x + 1) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 16, 84, 412, 1416, 3640, 7928, 15384, 27352, 45432}, 30] (* Harvey P. Dale, Apr 16 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 29 2010
STATUS
approved