A252823 Number of n X 3 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.

4, 18, 81, 340, 1238, 3891, 10761, 26764, 60988, 129236, 257653, 487744, 883142, 1538541, 2591269, 4236040, 6743492, 10483190, 15951849, 23807612, 34911302, 50375655, 71623633, 100457012, 139136540, 190475064, 257945133, 345802696

Offset: 1

Author

R. H. Hardin, Dec 22 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A252828.

Formula

Empirical: a(n) = (1/90720)*n^9 + (1/2520)*n^8 + (19/3780)*n^7 + (1/45)*n^6 + (157/4320)*n^5 + (31/180)*n^4 + (28507/45360)*n^3 + (769/2520)*n^2 + (1783/630)*n.

Conjectures from Colin Barker, Dec 06 2018: (Start)

G.f.: x*(4 - 22*x + 81*x^2 - 140*x^3 + 163*x^4 - 137*x^5 + 75*x^6 - 23*x^7 + 3*x^8) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)