A252932 Number of n X 2 nonnegative integer arrays with upper left 0 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.

2, 5, 13, 34, 83, 176, 329, 558, 879, 1308, 1861, 2554, 3403, 4424, 5633, 7046, 8679, 10548, 12669, 15058, 17731, 20704, 23993, 27614, 31583, 35916, 40629, 45738, 51259, 57208, 63601, 70454, 77783, 85604, 93933, 102786, 112179, 122128, 132649, 143758

Offset

1,1

Links

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

Formula

Empirical: a(n) = (8/3)*n^3 - 18*n^2 + (145/3)*n - 42 for n>2.

Conjectures from Colin Barker, Dec 07 2018: (Start)

G.f.: x*(2 - 3*x + 5*x^2 + 4*x^3 + 7*x^4 + x^5) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.

(End)

Example

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

Crossrefs

Column 2 of A252938.

Sequence in context: A104589 A154101 A122024 * A318234 A371426 A027931

Adjacent sequences: A252929 A252930 A252931 * A252933 A252934 A252935

Keyword

nonn

Author

R. H. Hardin, Dec 24 2014

Status

approved