A242279 Number of inequivalent (mod D_4) ways four checkers can be placed on an n X n board.

1, 23, 252, 1666, 7509, 26865, 79920, 209096, 491425, 1064575, 2150076, 4104738, 7458437, 13005041, 21857984, 35598880, 56353185, 87019191, 131364700, 194364050, 282314901, 403316353, 567402672, 787201416, 1078078209, 1459020095, 1952782300, 2587048786, 3394568325

Offset

2,2

Links

Heinrich Ludwig, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (4,-1,-16,19,20,-45,0,45,-20,-19,16,1,-4,1).

Formula

a(n) = (n^8 - 6*n^6 + 40*n^4 - 48*n^3 + 16*n^2 + IF(MOD(n, 2) = 1)*(14*n^4 - 48*n^3 + 34*n^2 - 3))/192.

G.f.: x^2*(1 + 19*x + 161*x^2 + 697*x^3 + 1446*x^4 + 2070*x^5 + 1422*x^6 + 766*x^7 + 105*x^8 + 31*x^9 + x^10 + x^11) / ((1-x)^9 * (1+x)^5). - Vaclav Kotesovec, May 10 2014

a(n) = A054772(n, 4), n >= 2. - Wolfdieter Lang, Oct 03 2016

Mathematica

CoefficientList[Series[x^2*(1 + 19*x + 161*x^2 + 697*x^3 + 1446*x^4 + 2070*x^5 + 1422*x^6 + 766*x^7 + 105*x^8 + 31*x^9 + x^10 + x^11) / ((1-x)^9 * (1+x)^5), {x, 0, 20}], x] (* Vaclav Kotesovec, May 10 2014 *)
LinearRecurrence[{4, -1, -16, 19, 20, -45, 0, 45, -20, -19, 16, 1, -4, 1}, {0, 0, 1, 23, 252, 1666, 7509, 26865, 79920, 209096, 491425, 1064575, 2150076, 4104738}, 40] (* Harvey P. Dale, May 06 2018 *)

Crossrefs

Cf. A054252, A008805, A014409, A082966, A242358, A019318, A054772.

Sequence in context: A268747 A158970 A161472 * A003910 A003911 A061977

Adjacent sequences: A242276 A242277 A242278 * A242280 A242281 A242282

Keyword

nonn,easy

Author

Heinrich Ludwig, May 10 2014

Status

approved