A201248 Number of ways to place 7 non-attacking ferses on an n X n board.

0, 0, 0, 216, 38070, 1314600, 21191208, 207830308, 1442794332, 7775083960, 34530764200, 131660992164, 443702617356, 1350258600008, 3771242866680, 9789675562020, 23856321869260, 55015308882264, 120855465245464, 254284702668580, 514791197224860, 1006655249550696

Offset

1,4

Comments

Fers is a leaper [1,1].

Links

Table of n, a(n) for n=1..22.

V. Kotesovec, Non-attacking chess pieces

Index entries for linear recurrences with constant coefficients, signature (15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1).

Formula

a(n) = n^14/5040 - n^12/48 + n^11/30 + 673n^10/720 - 17n^9/6 - 1019n^8/48 + 197n^7/2 + 9772n^6/45 - 3443n^5/2 + 47n^4/4 + 74259n^3/5 - 1816352n^2/105 - 49376n + 90660, n>=6.

G.f.: 2*x^4*(125*x^16 - 1785*x^15 + 11715*x^14 - 50121*x^13 + 158605*x^12 - 367485*x^11 + 570175*x^10 - 533381*x^9 + 460395*x^8 - 1262515*x^7 + 2731225*x^6 - 1795227*x^5 - 5484089*x^4 - 2685639*x^3 - 383115*x^2 - 17415*x - 108)/(x-1)^15.

Prog

(PARI) a(n)=if(n>5, n^14/5040-n^12/48+n^11/30+673*n^10/720-17*n^9/6-1019*n^8/48+197*n^7/2+9772*n^6/45-3443*n^5/2+47*n^4/4+74259*n^3/5-1816352*n^2/105-49376*n+90660, [0, 0, 0, 216, 38070][n]) \\ Charles R Greathouse IV, May 16 2026

Crossrefs

Cf. A187239, A201243, A201244, A201245, A201246, A201247.

Sequence in context: A365629 A078204 A230466 * A207553 A207547 A207314

Adjacent sequences: A201245 A201246 A201247 * A201249 A201250 A201251

Keyword

nonn,easy

Author

Vaclav Kotesovec, Nov 28 2011

Status

approved