A141582 a(n) = number of ways to dispose two pawns on a chessboard of size n X n (two dispositions are equivalent if one can be rotated or reflected to give the other one).

0, 0, 2, 8, 21, 48, 93, 168, 278, 440, 660, 960, 1347, 1848, 2471, 3248, 4188, 5328, 6678, 8280, 10145, 12320, 14817, 17688, 20946, 24648, 28808, 33488, 38703, 44520, 50955, 58080, 65912, 74528, 83946, 94248, 105453, 117648, 130853, 145160, 160590, 177240

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

For n even, a(n) = n * (n^3 + 6*n -4) / 16; for n odd a(n) = (n^2-1) * (n^2 + 7) / 16.

a(n) = 3*a(n-1)-a(n-2)-5*a(n-3)+5*a(n-4)+a(n-5)-3*a(n-6)+a(n-7) for n>6. - Colin Barker, Feb 21 2015

G.f.: -x^2*(3*x^3-x^2+2*x+2) / ((x-1)^5*(x+1)^2). - Colin Barker, Feb 21 2015

Example

For n = 2, two ways: either two pawns on any edge, or two pawns on any diagonal, hence a(2) = 2.

Prog

(PARI) concat([0, 0], Vec(-x^2*(3*x^3-x^2+2*x+2)/((x-1)^5*(x+1)^2) + O(x^100))) \\ Colin Barker, Feb 21 2015

Crossrefs

Sequence in context: A051744 A062443 A275740 * A192692 A182704 A000160

Adjacent sequences: A141579 A141580 A141581 * A141583 A141584 A141585

Keyword

easy,nonn

Author

Philippe Lallouet (philip.lallouet(AT)orange.fr), Aug 19 2008

Extensions

Typo in data fixed, and leading zeros added by Colin Barker, Feb 21 2015

Status

approved