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

1,1

Links

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

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)

Example

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

Crossrefs

Column 3 of A252828.

Sequence in context: A063881 A264004 A282708 * A264191 A257060 A181610

Adjacent sequences: A252820 A252821 A252822 * A252824 A252825 A252826

Keyword

nonn

Author

R. H. Hardin, Dec 22 2014

Status

approved