A253007 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 increasing by 0 or 1 with every step right, diagonally se or down.

1, 1, 1, 1, 124, 3423, 33533, 158877, 490403, 1156178, 2286874, 4013538, 6467242, 9779058, 14080058, 19501314, 26173898, 34228882, 43797338, 55010338, 67998954, 82894258, 99827322, 118929218, 140331018, 164163794, 190558618, 219646562

Offset

1,5

Links

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

Formula

Empirical: a(n) = (65536/3)*n^3 - 422912*n^2 + (8343128/3)*n - 6208382 for n>9.

Conjectures from Colin Barker, Dec 08 2018: (Start)

G.f.: x*(1 - 3*x + 3*x^2 - x^3 + 123*x^4 + 2930*x^5 + 20582*x^6 + 44788*x^7 + 42525*x^8 + 17119*x^9 + 2605*x^10 + 375*x^11 + 25*x^12) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>13.

(End)

Example

Some solutions for n=6:
..0..0..1..1....0..0..0..0....0..0..0..0....0..1..1..2....0..0..0..1
..0..0..1..1....0..1..1..1....1..1..1..1....0..1..1..2....0..0..0..1
..1..1..1..1....1..1..2..2....1..1..2..2....0..1..1..2....0..0..1..1
..2..2..2..2....1..1..2..2....1..2..2..2....1..1..1..2....0..0..1..2
..2..2..2..2....1..1..2..2....1..2..2..2....1..1..1..2....0..1..1..2
..2..2..2..2....1..1..2..2....1..2..2..2....1..1..1..2....1..1..2..2

Crossrefs

Column 4 of A253011.

Sequence in context: A260097 A232796 A263544 * A293084 A289299 A035816

Adjacent sequences: A253004 A253005 A253006 * A253008 A253009 A253010

Keyword

nonn

Author

R. H. Hardin, Dec 25 2014

Status

approved