A172208 Number of ways to place 4 nonattacking bishops on a 4 X n board.

1, 9, 61, 260, 927, 2578, 5965, 12066, 22135, 37678, 60457, 92488, 136043, 193650, 268093, 362412, 479903, 624118, 798865, 1008208, 1256467, 1548218, 1888293, 2281780, 2734023, 3250622, 3837433, 4500568, 5246395, 6081538, 7012877

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

Crossrefs

Cf. A172127, A061990, A172207.

Programs

Mathematica

CoefficientList[Series[-1 (2 x^12 - 2 x^11 + 4 x^10 - 24 x^9 + 50 x^8 - 10 x^7 + 41 x^6 - 23 x^5 + 152 * x^4 + 35 x^3 + 26  x^2 + 4 x + 1) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)
LinearRecurrence[{5,-10,10,-5,1},{1,9,61,260,927,2578,5965,12066,22135,37678,60457,92488,136043},40] (* Harvey P. Dale, Dec 13 2021 *)

Formula

a(n) = (32*n^4 -336*n^3 +1702*n^2 -4701*n +5844) / 3, n>=9.

G.f.: -x * (2*x^12 -2*x^11 +4*x^10 -24*x^9 +50*x^8 -10*x^7 +41*x^6 -23*x^5 +152*x^4 +35*x^3 +26*x^2 +4*x+1) / (x-1)^5. - Vaclav Kotesovec, Mar 25 2010