A172207 Number of ways to place 3 nonattacking bishops on a 3 X n board.

1, 6, 26, 86, 211, 426, 758, 1234, 1881, 2726, 3796, 5118, 6719, 8626, 10866, 13466, 16453, 19854, 23696, 28006, 32811, 38138, 44014, 50466, 57521, 65206, 73548, 82574, 92311, 102786, 114026, 126058, 138909, 152606, 167176, 182646, 199043, 216394, 234726, 254066

Offset: 1

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

• nonn
• easy

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 (4,-6,4,-1).

Crossrefs

Cf. A172124, A061989, A047659, A061996.

Programs

Mathematica

CoefficientList[Series[(2 x^6 + 14 x^3 + 8 x^2 + 2 x + 1) / (x - 1)^4, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)

Formula

a(n) = (9n^3 - 45n^2 + 106n - 108)/2, n>=4.

G.f.: x*(2*x^6+14*x^3+8*x^2+2*x+1)/(x-1)^4. - Vaclav Kotesovec, Mar 25 2010