A253491 Number of (n+1) X (4+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.

3639, 5386, 6476, 10477, 19475, 40117, 89339, 211597, 527555, 1373797, 3709259, 10309117, 29295635, 84629077, 247377179, 729117037, 2161327715, 6431941957, 19191749099, 57367099357, 171685007795, 514222448437, 1541002201019

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>6.

Empirical: a(n) = 49*3^(n-1) + 794*2^(n-1) + 2802 for n>3.

Conjectures from Colin Barker, Dec 15 2018: (Start)

G.f.: x*(3639 - 16448*x + 14189*x^2 + 9033*x^3 - 4467*x^4 - 342*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).

a(n) = 2802 + 397*2^n + 49*3^(n-1) for n>3.

(End)

Example

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

Crossrefs

Column 4 of A253495.

Sequence in context: A207288 A239992 A253498 * A253452 A253464 A015294

Adjacent sequences: A253488 A253489 A253490 * A253492 A253493 A253494

Keyword

nonn

Author

R. H. Hardin, Jan 02 2015

Status

approved