A229450 Number of 7 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

30, 142, 625, 2402, 8024, 23610, 62205, 149031, 329106, 677706, 1314145, 2419348, 4257692, 7203590, 11773293, 18662385, 28789446, 43346358, 63855729, 92235910, 130874080, 182707874, 251316029, 341018523, 456986682, 605363730, 793396257

Offset

1,1

Links

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

Formula

Empirical: a(n) = (95/1008)*n^7 - (241/360)*n^6 + (232/45)*n^5 - (1061/72)*n^4 + (5771/144)*n^3 - (7217/180)*n^2 + (18133/420)*n - 3.

Conjectures from Colin Barker, Sep 17 2018: (Start)

G.f.: x*(30 - 98*x + 329*x^2 - 302*x^3 + 456*x^4 - 66*x^5 + 123*x^6 + 3*x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Row 7 of A229445.

Sequence in context: A267904 A218407 A347222 * A124958 A126417 A135175

Adjacent sequences: A229447 A229448 A229449 * A229451 A229452 A229453

Keyword

nonn

Author

R. H. Hardin, Sep 23 2013

Status

approved