A082966 Number of inequivalent ways (mod D_4) three checkers can be placed on an n X n board.

0, 1, 16, 77, 319, 920, 2397, 5278, 10874, 20355, 36390, 61171, 99441, 154882, 235179, 346060, 499172, 702933, 974124, 1324585, 1777555, 2349116, 3070441, 3962762, 5066814, 6409975, 8044322, 10004463, 12355749, 15141190, 18441495, 22309336, 26843016, 32106217

Offset: 1

Author

Vladeta Jovovic, May 27 2003

Keywords

• nonn
• easy

Links

• Erich Friedman, Illustration of initial terms
• Index entries for linear recurrences with constant coefficients, signature (3,1,-11,6,14,-14,-6,11,-1,-3,1).

Crossrefs

Cf. A014409, A054252, A242279, A242358, A054247.

Programs

Mathematica

Rest@ CoefficientList[Series[x^2*(x^8 - x^7 - 4 x^6 - 55 x^5 - 56 x^4 - 83 x^3 - 28 x^2 - 13 x - 1)/((x - 1)^7*(x + 1)^4), {x, 0, 34}], x] (* Michael De Vlieger, Oct 03 2016 *)

Formula

a(n) = (1/48)*(n-1)*(n^5+n^4-2*n^3+14*n^2-5*n+3) if n is odd;

a(n) = (1/48)*n*(n-1)*(n^2-n+2)*(n^2+2*n-2) if n is even.

G.f.: x^2*(x^8-x^7-4*x^6-55*x^5-56*x^4-83*x^3-28*x^2-13*x-1) / ((x-1)^7*(x+1)^4). - Colin Barker, Jul 11 2013

a(n) = A054247(n, 3) = A054247(n, n^2-3), n >= 1. - Wolfdieter Lang, Oct 03 2016

E.g.f.: (x*(3 + 24*x + 88*x^2 + 62*x^3 + 15*x^4 + x^5)*cosh(x) + (-3 + 39*x^2 + 80*x^3 + 62*x^4 + 15*x^5 + x^6)*sinh(x))/48. - Stefano Spezia, Apr 14 2022

Extensions

More terms from Colin Barker, Jul 11 2013