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A253000
Number of n X 4 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
1, 1, 1, 1, 69, 1132, 7235, 25233, 63135, 129133, 231419, 378185, 577623, 837925, 1167283, 1573889, 2065935, 2651613, 3339115, 4136633, 5052359, 6094485, 7271203, 8590705, 10061183, 11690829, 13487835, 15460393, 17616695, 19964933, 22513299
OFFSET
1,5
LINKS
FORMULA
Empirical: a(n) = (4096/3)*n^3 - 22816*n^2 + (388490/3)*n - 249567 for n>6.
Conjectures from Colin Barker, Dec 08 2018: (Start)
G.f.: x*(1 - 3*x + 3*x^2 - x^3 + 68*x^4 + 859*x^5 + 3118*x^6 + 2810*x^7 + 1154*x^8 + 183*x^9) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>10.
(End)
EXAMPLE
Some solutions for n=6:
..0..0..0..0....0..0..0..0....0..0..0..0....0..1..1..1....0..1..1..2
..0..0..0..1....1..1..1..1....0..1..1..1....0..1..1..1....1..1..1..2
..0..1..1..1....1..1..2..2....1..1..1..2....1..1..2..2....1..1..1..2
..0..1..2..2....1..1..2..2....2..2..2..2....1..2..2..2....1..1..1..2
..1..1..2..2....1..2..2..2....2..2..2..2....1..2..2..2....1..1..1..2
..2..2..2..2....2..2..2..2....2..2..2..2....2..2..2..2....2..2..2..2
CROSSREFS
Column 4 of A253004.
Sequence in context: A160831 A254683 A095255 * A295212 A264283 A333034
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 25 2014
STATUS
approved