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A252999 Number of n X 3 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 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
0, 0, 0, 1, 34, 279, 1028, 2601, 5318, 9499, 15464, 23533, 34026, 47263, 63564, 83249, 106638, 134051, 165808, 202229, 243634, 290343, 342676, 400953, 465494, 536619, 614648, 699901, 792698, 893359, 1002204, 1119553, 1245726, 1381043, 1525824 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
LINKS
FORMULA
Empirical: a(n) = (160/3)*n^3 - 708*n^2 + (9539/3)*n - 4831 for n>4.
Conjectures from Colin Barker, Dec 08 2018: (Start)
G.f.: x^4*(1 + 30*x + 149*x^2 + 112*x^3 + 28*x^4) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.
(End)
EXAMPLE
Some solutions for n=6:
..0..0..0....0..1..1....0..1..2....0..0..1....0..0..1....0..0..1....0..1..1
..0..0..1....1..1..2....1..1..2....0..1..1....0..1..1....1..1..1....1..1..2
..0..0..1....1..2..2....1..1..2....0..1..2....1..1..1....1..1..1....1..1..2
..1..1..1....2..2..2....1..2..2....1..1..2....1..1..2....1..1..2....1..1..2
..1..1..2....2..2..2....1..2..2....1..2..2....2..2..2....1..2..2....1..2..2
..2..2..2....2..2..2....2..2..2....2..2..2....2..2..2....2..2..2....2..2..2
CROSSREFS
Column 3 of A253004.
Sequence in context: A228284 A248076 A301543 * A229327 A209891 A027006
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 25 2014
STATUS
approved

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Last modified June 23 11:27 EDT 2024. Contains 373644 sequences. (Running on oeis4.)