A252824 Number of n X 4 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

Author

R. H. Hardin, Dec 22 2014

Keywords

• nonn

Comments

Column 4 of A252828.

Examples

			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
		

Links

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

Crossrefs

Cf. A252828.

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.