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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Row 7 of A229445.
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)
Comments