A201246 Number of ways to place 5 non-attacking ferses on an n X n board.

0, 0, 12, 780, 16286, 159452, 992412, 4567836, 16959488, 53617596, 149618794, 377841356, 879314442, 1911495356, 3922051616, 7657895196, 14321764860, 25791609308, 44921419134, 75946019596, 125016699158, 200899440924, 315872975684, 486869916572, 736910896536

Offset

1,3

Comments

Fers is a leaper [1,1].

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

V. Kotesovec, Non-attacking chess pieces, 6ed, p.415

Formula

a(n) = n^10/120 - 5n^8/12 + 2n^7/3 + 191n^6/24 - 24n^5 - 661n^4/12 + 880n^3/3 - 937n^2/15 - 1176n + 1436, n>=4.

G.f.: 2x^3*(11x^11 - 135x^10 + 549x^9 - 993x^8 + 1172x^7 - 2968x^6 + 7085x^5 - 4715x^4 - 10613x^3 - 4183x^2 - 324x - 6)/(x-1)^11.

Mathematica

CoefficientList[Series[2 x^2 (11 x^11 - 135 x^10 + 549 x^9 - 993 x^8 + 1172 x^7 - 2968 x^6 + 7085 x^5 - 4715x^4 - 10613 x^3 - 4183 x^2- 324 x - 6)/(x-1)^11, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 30 2013 *)

Crossrefs

Cf. A172129, A201243, A201244, A201245, A201247, A201248.

Sequence in context: A273033 A276636 A284769 * A291999 A282437 A285150

Adjacent sequences: A201243 A201244 A201245 * A201247 A201248 A201249

Keyword

nonn,easy

Author

Vaclav Kotesovec, Nov 28 2011

Status

approved