A252979 Number of n X 4 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down.

3, 13, 33, 68, 1247, 8487, 27905, 62977, 114433, 182273, 266497, 367105, 484097, 617473, 767233, 933377, 1115905, 1314817, 1530113, 1761793, 2009857, 2274305, 2555137, 2852353, 3165953, 3495937, 3842305, 4205057, 4584193, 4979713, 5391617

Offset

1,1

Links

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

Formula

Empirical: a(n) = 8192*n^2 - 87808*n + 241153 for n>6.

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

G.f.: x*(3 + 4*x + 3*x^2 + 5*x^3 + 1129*x^4 + 4917*x^5 + 6117*x^6 + 3476*x^7 + 730*x^8) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.

(End)

Example

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

Crossrefs

Column 4 of A252983.

Sequence in context: A147137 A146230 A166805 * A332366 A033943 A026084

Adjacent sequences: A252976 A252977 A252978 * A252980 A252981 A252982

Keyword

nonn

Author

R. H. Hardin, Dec 25 2014

Status

approved