A172213 Number of ways to place 4 nonattacking knights on a 4 X n board.

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

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 (5,-10,10,-5,1).

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

Cf. A172135, A061990, A172212.

Sequence in context: A218082 A159501 A172219 * A231941 A118675 A223962

Adjacent sequences: A172210 A172211 A172212 * A172214 A172215 A172216

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Status

approved