A252824 Number of nX4 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down

8, 53, 340, 1920, 9075, 36292, 125892, 387849, 1082111, 2777103, 6637625, 14922949, 31813809, 64737785, 126429330, 238046837, 433778614, 767506845, 1322268502, 2223460226, 3656986483, 5893853502, 9323072932, 14495166797, 22179067861

Offset

1,1

Comments

Column 4 of A252828

Links

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

Formula

Empirical: a(n) = (29/479001600)*n^12 + (29/8870400)*n^11 + (3083/43545600)*n^10 + (233/290304)*n^9 + (75539/14515200)*n^8 + (56551/2419200)*n^7 + (4051409/43545600)*n^6 + (123049/483840)*n^5 + (5473861/10886400)*n^4 + (1817149/1814400)*n^3 + (5653001/1663200)*n^2 + (23839/13860)*n + 1

Example

Some solutions for n=4
..0..0..1..1....0..0..1..2....0..1..1..2....0..1..2..2....0..0..0..0
..0..1..2..2....0..1..2..3....1..2..2..2....1..1..2..2....0..0..0..1
..1..2..3..3....1..2..3..3....2..2..2..2....1..2..3..3....1..1..1..2
..2..3..4..4....2..3..4..4....2..3..3..3....1..2..3..4....1..2..2..3

Crossrefs

Sequence in context: A110099 A297334 A091870 * A054418 A293115 A337554

Adjacent sequences: A252821 A252822 A252823 * A252825 A252826 A252827

Keyword

nonn

Author

R. H. Hardin, Dec 22 2014

Status

approved