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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A027931 A218481

Adjacent sequences:  A252929 A252930 A252931 * A252933 A252934 A252935

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 24 2014

STATUS

approved

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Last modified March 29 05:32 EDT 2020. Contains 333105 sequences. (Running on oeis4.)