A201245 Number of ways to place 4 non-attacking ferses on an n X n board.

0, 0, 29, 661, 6285, 35378, 143787, 468529, 1301351, 3202970, 7170593, 14872997, 28969129, 53527866, 94568255, 160741233, 264175507, 421511954, 655152581, 994751765, 1478979173, 2157585442, 3093803379, 4367119121, 6076449375, 8343762538, 11318183177

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^8 - 30n^6 + 48n^5 + 299n^4 - 912n^3 - 462n^2 + 4368n - 4200)/24, n>=3.

G.f.: -x^3*(2*x^8 - 55*x^7 + 230*x^6 - 254*x^5 - 225*x^4 + 173*x^3 + 1380*x^2 + 400*x + 29)/(x-1)^9.

Mathematica

CoefficientList[Series[- x^2 (2 x^8 - 55 x^7 + 230 x^6 - 254 x^5 - 225 x^4 + 173 x^3 + 1380 x^2 + 400 x + 29)/(x-1)^9, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 30 2013 *)

Crossrefs

Cf. A172127, A201243, A201244, A201246, A201247, A201248.

Sequence in context: A329016 A072080 A263515 * A063044 A062560 A135995

Adjacent sequences: A201242 A201243 A201244 * A201246 A201247 A201248

Keyword

nonn,easy

Author

Vaclav Kotesovec, Nov 28 2011

Status

approved