A252934 Number of n X 4 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.

8, 34, 153, 711, 3067, 10920, 30818, 70640, 138558, 242764, 391450, 592808, 855030, 1186308, 1594834, 2088800, 2676398, 3365820, 4165258, 5082904, 6126950, 7305588, 8627010, 10099408, 11730974, 13529900, 15504378, 17662600, 20012758, 22563044

Offset

1,1

Links

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

Formula

Empirical: a(n) = (4096/3)*n^3 - 18720*n^2 + (269642/3)*n - 149376 for n>6.

Conjectures from Colin Barker, Dec 07 2018: (Start)

G.f.: x*(8 + 2*x + 65*x^2 + 271*x^3 + 1013*x^4 + 2340*x^5 + 2849*x^6 + 1331*x^7 + 293*x^8 + 20*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=4:
..0..0..0..0....0..0..1..1....0..0..1..1....0..0..1..1....0..0..1..1
..0..0..0..0....1..1..1..2....1..1..1..2....0..0..1..2....0..1..1..2
..0..1..1..1....1..1..1..2....1..1..2..2....1..1..1..2....0..1..2..2
..0..1..1..2....1..2..2..2....1..1..2..3....2..2..2..2....0..1..2..3

Crossrefs

Column 4 of A252938.

Sequence in context: A126395 A335749 A227330 * A229398 A223015 A222796

Adjacent sequences: A252931 A252932 A252933 * A252935 A252936 A252937

Keyword

nonn

Author

R. H. Hardin, Dec 24 2014

Status

approved