A251293 Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock summing to 3 6 or 9.

84, 444, 2356, 12556, 67204, 361244, 1950036, 10570156, 57525924, 314285244, 1723404916, 9483540556, 52358197444, 289959524444, 1610402286996, 8967708907756, 50059450561764, 280064572814844, 1570043088196276

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 10*a(n-1) - 21*a(n-2) - 20*a(n-3).

Conjectures from Colin Barker, Nov 28 2018: (Start)

G.f.: 4*x*(21 - 99*x - 80*x^2) / ((1 - 5*x)*(1 - 5*x - 4*x^2)).

a(n) = (1/41)*2^(-n)*(41*10^(1+n) + (123-19*sqrt(41))*(5-sqrt(41))^n + (5+sqrt(41))^n*(123+19*sqrt(41))).

(End)

Example

Some solutions for n=4:
..0..1....2..2....2..3....2..0....3..0....2..1....3..0....1..1....1..0....3..3
..2..0....0..2....1..0....1..0....0..0....0..3....0..3....1..0....2..0....0..0
..0..1....1..0....1..1....3..2....3..3....3..0....1..2....0..2....1..3....0..3
..0..2....1..1....3..1....3..1....0..3....2..1....0..0....1..0....3..2....0..0
..0..1....0..1....0..2....0..2....1..2....3..3....2..1....0..2....2..2....3..3

Crossrefs

Column 1 of A251300.

Sequence in context: A083986 A189543 A251300 * A251254 A349682 A064198

Adjacent sequences: A251290 A251291 A251292 * A251294 A251295 A251296

Keyword

nonn

Author

R. H. Hardin, Dec 01 2014

Status

approved