A274723 Number of n X 3 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

5, 24, 68, 260, 1040, 4132, 16524, 66088, 264332, 1057316, 4229264, 16917028, 67668108, 270672424, 1082689676, 4330758692, 17323034768, 69292139044, 277168556172, 1108674224680, 4434696898700, 17738787594788, 70955150379152

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 4*a(n-2) + a(n-3) - 3*a(n-4) - 4*a(n-5) for n>7.

Empirical g.f.: x*(5 + 9*x - 24*x^2 - 45*x^3 - 21*x^4 - 4*x^5 + 8*x^6) / ((1 - x)*(1 + x)*(1 - 4*x)*(1 + x + x^2)). - Colin Barker, Jan 30 2019

Example

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

Crossrefs

Column 3 of A274728.

Sequence in context: A258290 A205669 A101147 * A006328 A213766 A000347

Adjacent sequences: A274720 A274721 A274722 * A274724 A274725 A274726

Keyword

nonn

Author

R. H. Hardin, Jul 03 2016

Status

approved