A265233 Number of 3 X n arrays containing n copies of 0..2 with no equal vertical neighbors and new values introduced sequentially from 0.

1, 1, 7, 56, 495, 4686, 46456, 475392, 4976271, 52977890, 571434402, 6228357312, 68468597544, 758063599632, 8443936740960, 94545206802816, 1063391499647631, 12007844534804202, 136068111377744686, 1546682224461979920, 17630279034262961010, 201470426310372260580

Offset: 0

Author

R. H. Hardin, Dec 06 2015

Keywords

• nonn

Comments

Row 3 of A265232.

Examples

			Some solutions for n=4
..0..1..0..2....0..1..2..2....0..1..0..0....0..1..1..2....0..1..1..2
..2..0..2..0....2..0..1..0....2..2..2..2....1..2..2..0....2..0..0..0
..1..1..1..2....0..1..2..1....1..1..0..1....0..0..1..2....1..1..2..2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 0..106

Crossrefs

Cf. A265232.

Formula

Conjecture: n^2*a(n) +(-19*n^2+19*n-6)*a(n-1) +96*(n-1)^2*a(n-2) -144*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Dec 08 2015

Conjecture: a(n) ~ 2^(2*n - 1) * 3^(n - 1/2) / (Pi*n). - Vaclav Kotesovec, Mar 08 2023

If conjectured recurrence is true then ogf = (hypergeom([1/3,2/3],[1],27*x*(4*x-1)^2)+5)/6. - Mark van Hoeij, Nov 28 2024

Extensions

a(0)=1 prepended by Alois P. Heinz, Nov 28 2024