A220639 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly one king-move neighbor.

1, 3, 40, 369, 3755, 37320, 373177, 3725843, 37213728, 371654153, 3711809483, 37070598992, 370232236753, 3697589375491, 36928628181272, 368814220524417, 3683427651446923, 36787191180049816, 367401660507886793, 3669320102980547411, 36646296045314442000

Offset

0,2

Comments

Column 3 of A220644.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500 (terms n = 1..210 from R. H. Hardin)

Index entries for linear recurrences with constant coefficients, signature (8,22,-20,-16,10,-3).

Formula

Empirical: a(n) = 8*a(n-1) +22*a(n-2) -20*a(n-3) -16*a(n-4) +10*a(n-5) -3*a(n-6).

G.f.: -(x^4-3*x^3+6*x^2+5*x-1)/((x-1)*(3*x^5-7*x^4+9*x^3+29*x^2+7*x-1)). - Alois P. Heinz, Jun 03 2014

Example

Some solutions for n=3 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10)
..0..6..4....0..0..0....6..4..0....8..9..0....8..9..0....8..0..0....6..4..0
..9..0..8....9..0..0....8..6..4....2..9..1....2..0..1....2..0..0....0..0..0
..0..1..2....0..1..0....2..6..4....0..0..1....6..4..0....0..6..4....6..4..0

Maple

gf:= -(x^4-3*x^3+6*x^2+5*x-1)/((x-1)*(3*x^5-7*x^4+9*x^3+29*x^2+7*x-1)):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..30);  # Alois P. Heinz, Jun 03 2014

Mathematica

LinearRecurrence[{8, 22, -20, -16, 10, -3}, {3, 40, 369, 3755, 37320, 373177}, 30] (* Harvey P. Dale, Nov 17 2013 *)

Crossrefs

Sequence in context: A165386 A293501 A002700 * A355373 A337692 A331795

Adjacent sequences: A220636 A220637 A220638 * A220640 A220641 A220642

Keyword

nonn,easy

Author

R. H. Hardin, Dec 17 2012

Status

approved