A201244 Number of ways to place 3 non-attacking ferses on an n X n board.

0, 0, 38, 340, 1630, 5552, 15210, 35828, 75530, 146240, 264702, 453620, 742918, 1171120, 1786850, 2650452, 3835730, 5431808, 7545110, 10301460, 13848302, 18357040, 24025498, 31080500, 39780570, 50418752, 63325550, 78871988, 97472790, 119589680, 145734802

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

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = (n-2)*(n^5 + 2n^4 - 11n^3 + 2n^2 + 54n - 60)/6, n>=2.

G.f.: -2x^3*(x^5 + 3x^4 - 24x^3 + 24x^2 + 37x + 19)/(x-1)^7.

a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Vincenzo Librandi, Apr 30 2013

Mathematica

CoefficientList[Series[- 2 x^2 (x^5 + 3 x^4 - 24 x^3 + 24 x^2 + 37 x + 19) / (x-1)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 30 2013 *)

Prog

(Magma) I:=[0, 0, 38, 340, 1630, 5552, 15210, 35828]; [n le 8 select I[n] else 7*Self(n-1)-21*Self(n-2)+35*Self(n-3)-35*Self(n-4)+21*Self(n-5)-7*Self(n-6)+Self(n-7): n in [1..40]]; /* or */ [0] cat [(n-2)*(n^5+2*n^4-11*n^3 +2*n^2+54*n-60)/6: n in [2..35]]; // Vincenzo Librandi, Apr 30 2013

Crossrefs

Cf. A172124, A201243, A201245, A201246, A201247, A201248.

Sequence in context: A297799 A204070 A242209 * A240263 A156661 A249711

Adjacent sequences: A201241 A201242 A201243 * A201245 A201246 A201247

Keyword

nonn,easy

Author

Vaclav Kotesovec, Nov 28 2011

Status

approved