A220640 Number of ways to reciprocally link elements of an n X 4 array either to themselves or to exactly one king-move neighbor.

1, 5, 172, 3755, 92801, 2226936, 53841725, 1299348473, 31371388772, 757341382671, 18283618480037, 441397115736816, 10656083384666537, 257256013409077661, 6210599281867691164, 149934463555725516099, 3619673802389322978937, 87385102146053809399912

Offset

0,2

Comments

Column 4 of A220644.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300 (terms n = 1..210 from R. H. Hardin)

Formula

Empirical: a(n) = 20*a(n-1) +114*a(n-2) -325*a(n-3) -340*a(n-4) +460*a(n-5) +245*a(n-6) -48*a(n-7) +2*a(n-8) -15*a(n-9).

G.f.: -(3*x^7 -x^6 +14*x^5 -58*x^4 -70*x^3 +42*x^2 +15*x-1) / (15*x^9 -2*x^8 +48*x^7 -245*x^6 -460*x^5 +340*x^4 +325*x^3 -114*x^2 -20*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)
..9..9..0..0....0..0..0..8....8..6..4..0....6..4..8..0....8..0..0..7
..8..1..1..0....9..7..0..2....2..0..8..8....0..0..2..0....2..8..3..0
..2..6..4..0....3..1..6..4....6..4..2..2....6..4..6..4....0..2..0..0

Maple

gf:= -(3*x^7 -x^6 +14*x^5 -58*x^4 -70*x^3 +42*x^2 +15*x-1) / (15*x^9 -2*x^8 +48*x^7 -245*x^6 -460*x^5 +340*x^4 +325*x^3 -114*x^2 -20*x+1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..30);  # Alois P. Heinz, Jun 03 2014

Crossrefs

Sequence in context: A231279 A210832 A206393 * A198711 A210927 A139986

Adjacent sequences: A220637 A220638 A220639 * A220641 A220642 A220643

Keyword

nonn

Author

R. H. Hardin, Dec 17 2012

Status

approved