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

0,3

Comments

Row 3 of A265232.

Links

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

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

Example

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

Crossrefs

Cf. A265232.

Sequence in context: A024091 A145302 A233669 * A165322 A082305 A144263

Adjacent sequences: A265230 A265231 A265232 * A265234 A265235 A265236

Keyword

nonn

Author

R. H. Hardin, Dec 06 2015

Extensions

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

Status

approved