A222308 Let P be a one-move "rider" with move set M={(1,2)}; a(n) is the number of non-attacking positions of two indistinguishable pieces P on an n X n board.

0, 6, 34, 114, 285, 602, 1127, 1940, 3126, 4790, 7040, 10006, 13819, 18634, 24605, 31912, 40732, 51270, 63726, 78330, 95305, 114906, 137379, 163004, 192050, 224822, 261612, 302750, 348551, 399370, 455545, 517456, 585464, 659974, 741370, 830082, 926517, 1031130, 1144351, 1266660, 1398510, 1540406, 1692824

Offset

1,2

Links

Table of n, a(n) for n=1..43.

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

S. Chaiken, C. R. H. Hanusa and T. Zaslavsky, A q-queens problem II. The square board, preprint, August 7, 2014. See Corollary 5.2.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).

Formula

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

G.f.: -x^2*(x^4+7*x^3+18*x^2+16*x+6) / ((x-1)^5*(x+1)^2). [Colin Barker, Feb 16 2013]

Mathematica

LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 6, 34, 114, 285, 602, 1127}, 50] (* Harvey P. Dale, Mar 09 2016 *)

Crossrefs

Sequence in context: A341290 A061616 A368757 * A166812 A262844 A166941

Adjacent sequences: A222305 A222306 A222307 * A222309 A222310 A222311

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 16 2013

Status

approved