A252817 Number of n X 5 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.

11, 81, 468, 2078, 7564, 23664, 65711, 165685, 385736, 839799, 1726761, 3379640, 6336411, 11439478, 19972358, 33843927, 55832593, 89905021, 141626554, 218683266, 331538662, 494251420, 725484265, 1049738089, 1498849798

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/259200)*n^10 + (1/6480)*n^9 + (149/60480)*n^8 + (163/7560)*n^7 + (10411/86400)*n^6 + (209/432)*n^5 + (17977/12960)*n^4 + (6043/3240)*n^3 + (37673/12600)*n^2 + (1423/1260)*n + 3.

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

G.f.: x*(11 - 40*x + 182*x^2 - 430*x^3 + 711*x^4 - 822*x^5 + 657*x^6 - 360*x^7 + 131*x^8 - 29*x^9 + 3*x^10) / (1 - x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

(End)

Example

Some solutions for n=4:
..0..1..1..2..3....0..1..2..3..3....0..1..1..2..3....0..0..1..2..3
..1..2..2..3..3....1..2..2..3..4....1..1..2..3..4....1..1..2..3..4
..2..3..3..4..4....2..2..2..3..4....1..2..3..4..4....1..2..2..3..4
..2..3..4..5..5....2..2..3..4..5....2..3..3..4..5....1..2..3..4..5

Crossrefs

Column 5 of A252820.

Sequence in context: A156847 A119364 A305826 * A210064 A323223 A211557

Adjacent sequences: A252814 A252815 A252816 * A252818 A252819 A252820

Keyword

nonn

Author

R. H. Hardin, Dec 22 2014

Status

approved