A252816 Number of n X 4 nonnegative integer arrays with upper left 0 and every value within 2 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

7, 40, 187, 684, 2078, 5490, 13015, 28299, 57338, 109549, 199168, 347035, 582831, 947837, 1498290, 2309416, 3480225, 5139158, 7450681, 10622926, 14916484, 20654460, 28233905, 38138745, 50954332, 67383747, 88265990, 114596197

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/8064)*n^8 + (1/288)*n^7 + (103/2880)*n^6 + (17/90)*n^5 + (703/1152)*n^4 + (451/288)*n^3 + (2869/3360)*n^2 + (209/120)*n + 2.

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

G.f.: x*(7 - 23*x + 79*x^2 - 147*x^3 + 176*x^4 - 138*x^5 + 67*x^6 - 18*x^7 + 2*x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

Example

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

Crossrefs

Column 4 of A252820.

Sequence in context: A365373 A263473 A055282 * A093737 A268402 A351529

Adjacent sequences: A252813 A252814 A252815 * A252817 A252818 A252819

Keyword

nonn

Author

R. H. Hardin, Dec 22 2014

Status

approved