A201238 Number of ways to place 4 non-attacking wazirs on an n X n toroidal board.

0, 0, 0, 228, 3850, 27225, 122892, 423152, 1213380, 3046025, 6907890, 14454972, 28330822, 52586065, 93218400, 158854080, 261593552, 418045617, 650576150, 988799100, 1471339170, 2147897257, 3081651412, 4352027760, 6057877500, 8321097785, 11290735962

Offset

1,4

Comments

Wazir is a leaper [0,1].

Links

Table of n, a(n) for n=1..27.

V. Kotesovec, Non-attacking chess pieces, 6ed, p.402

Formula

a(n) = n^2*(n^2-11)*(n^4 - 19n^2 + 114)/24, n>=5.

G.f.: x^4 * (8x^9 - 54x^8 + 189x^7 - 551x^6 + 1404x^5 - 2552x^4 + 2685x^3 - 783x^2 - 1798x - 228)/(x-1)^9.

Mathematica

CoefficientList[Series[x^3*(8 x^9 - 54 x^8 + 189 x^7 - 551 x^6 + 1404 x^5 - 2552 x^4 + 2685 x^3 - 783 x^2 - 1798 x - 228)/(x - 1)^9, {x, 0, 20}], x] (* Wesley Ivan Hurt, Jan 19 2017 *)

Crossrefs

Cf. A172227, A201236, A201237, A201239, A201240, A201241, A201242.

Sequence in context: A103837 A302755 A064245 * A220624 A098246 A091551

Adjacent sequences: A201235 A201236 A201237 * A201239 A201240 A201241

Keyword

nonn,easy

Author

Vaclav Kotesovec, Nov 28 2011

Status

approved