A243718 Number of inequivalent (mod D_8) ways to place 3 nonattacking knights on an n X n board.

1, 9, 40, 195, 618, 1751, 4075, 8794, 17015, 31268, 53666, 88781, 140200, 215405, 320013, 465436, 659965, 920114, 1257580, 1695303, 2249206, 2950131, 3819135, 4896590, 6209683, 7810096, 9732230, 12041009, 14779220, 18027113, 21837121, 26307056, 31500345

Offset

2,2

Links

Heinrich Ludwig, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (3,1,-11,6,14,-14,-6,11,-1,-3,1).

Formula

a(n) = (n^6 - 27*n^4 + 80*n^3 + 158*n^2 - 1028*n + 1200 + (1 - (-1)^n)/2*(8*n^3 - 9*n^2 - 44*n + 45))/48 for n >= 4.

G.f.: -25 - 8*x + 3*x^3 + (25 - 67*x - 48*x^2 + 270*x^3 - 41*x^4 - 318*x^5 + 291*x^6 + 354*x^7 - 188*x^8 - 87*x^9 + 49*x^10) / ((1-x)^7*(1+x)^4). - Vaclav Kotesovec, Jun 19 2014

Mathematica

Drop[CoefficientList[Series[-25 - 8*x + 3*x^3 + (25 - 67*x - 48*x^2 + 270*x^3 - 41*x^4 - 318*x^5 + 291*x^6 + 354*x^7 - 188*x^8 - 87*x^9 + 49*x^10) / ((1-x)^7*(1+x)^4), {x, 0, 20}], x], 2] (* Vaclav Kotesovec, Jun 19 2014 *)

Crossrefs

Cf. A243716, A172134, A243717, A243719, A243720.

Sequence in context: A027137 A264106 A026629 * A086349 A359724 A026651

Adjacent sequences: A243715 A243716 A243717 * A243719 A243720 A243721

Keyword

nonn,easy

Author

Heinrich Ludwig, Jun 19 2014

Status

approved