A196431 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,0,3,4 for x=0,1,2,3,4.

3, 9, 25, 75, 213, 621, 1801, 5219, 15133, 43867, 127195, 368759, 1069105, 3099583, 8986391, 26053581, 75535111, 218993223, 634910491, 1840747761, 5336740123, 15472405305, 44857970049, 130053306249, 377053674603, 1093163086545

Offset

1,1

Comments

Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 0's, every 3 is next to 3 3's, every 4 is next to 4 4's.

Column 3 of A196436.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = a(n-1) + 3*a(n-2) + 5*a(n-3) + 6*a(n-4) + 4*a(n-5) - 5*a(n-6) - 5*a(n-7) - a(n-8) + a(n-9).

Empirical g.f.: x*(1 + x)*(3 + 3*x + 4*x^2 + 4*x^3 - 4*x^4 - 4*x^5 - x^6 + x^7) / (1 - x - 3*x^2 - 5*x^3 - 6*x^4 - 4*x^5 + 5*x^6 + 5*x^7 + x^8 - x^9). - Colin Barker, Mar 01 2018

Example

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

Crossrefs

Cf. A196436.

Sequence in context: A138574 A101499 A004665 * A244826 A183111 A132835

Adjacent sequences: A196428 A196429 A196430 * A196432 A196433 A196434

Keyword

nonn

Author

R. H. Hardin, Oct 02 2011

Status

approved