A222309 Let P be a one-move "rider" with move set M={(1,2)}; a(n) is the number of non-attacking positions of three indistinguishable pieces P on an n X n board.

0, 4, 70, 476, 1961, 6204, 16167, 37040, 76486, 146300, 262260, 446844, 728295, 1144836, 1742461, 2581184, 3730972, 5280660, 7331346, 10008700, 13453045, 17835884, 23345795, 30210096, 38675586, 49036364, 61608352, 76764380, 94901331, 116483700, 142002105, 172026624, 207155320, 248078756, 295517086, 350297244

Offset

1,2

Links

Table of n, a(n) for n=1..36.

S. Chaiken, C. R. H. Hanusa and T. Zaslavsky, A q-queens problem I. General theory, preprint, August 7, 2014.

Index entries for linear recurrences with constant coefficients, signature (3,1,-11,6,14,-14,-6,11,-1,-3,1).

Formula

a(n) = n^6/6 - 5*n^5/24 + n^4/16 - 11*n^3/48 + 7*n^2/48 + 1/32 + (-1)^n*(n^3/16 - n^2/16 - 1/32).

G.f.: -x^2*(x^8+17*x^7+126*x^6+354*x^5+591*x^4+507*x^3+262*x^2+58*x+4) / ((x-1)^7*(x+1)^4). [Colin Barker, Feb 16 2013]

Mathematica

LinearRecurrence[{3, 1, -11, 6, 14, -14, -6, 11, -1, -3, 1}, {0, 4, 70, 476, 1961, 6204, 16167, 37040, 76486, 146300, 262260}, 40] (* Harvey P. Dale, Oct 29 2016 *)

Crossrefs

Sequence in context: A101841 A274873 A281654 * A061609 A349457 A301586

Adjacent sequences: A222306 A222307 A222308 * A222310 A222311 A222312

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 16 2013

Status

approved