A194788 Number of ways to place 7 nonattacking kings on an n X n board.

0, 0, 0, 0, 242, 51504, 2484382, 44601420, 450193818, 3112919712, 16471667554, 71393226972, 265069706646, 869583076752, 2577681275622, 7020477731884, 17794428237522, 42397762374912, 95726217156906, 206149749502012, 425731784898894, 846919172059632

Offset

1,5

Links

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

V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

Formula

a(n) = (n^14 - 189n^12 + 252n^11 + 15211n^10 - 38640n^9 - 649215n^8 + 2408700n^7 + 14771764n^6 - 75856200n^5 - 144099396n^4 + 1198867488n^3 - 255900576n^2 - 7543005120n + 10617929280)/5040, n>=6. - Andrew Woods, Sep 02 2011

G.f.: 2*x^5*(1930*x^15 - 20052*x^14 + 87663*x^13 - 265681*x^12 + 816798*x^11 - 2117376*x^10 + 2865281*x^9 + 557737*x^8 - 6577818*x^7 + 3848604*x^6 + 8828017*x^5 - 9464319*x^4 - 6316750*x^3 - 868616*x^2 - 23937*x - 121)/ (x-1)^15. - Vaclav Kotesovec, Nov 06 2011

Crossrefs

Cf. A061995, A061996, A061997, A061998, A172158.

Sequence in context: A035748 A022153 A335611 * A338454 A055554 A214105

Adjacent sequences: A194785 A194786 A194787 * A194789 A194790 A194791

Keyword

nonn

Author

Andrew Woods, Sep 02 2011

Status

approved