A212777 Half the number of 0..3 arrays of length n+2 with second differences nonzero.

28, 99, 350, 1238, 4379, 15490, 54793, 193821, 685609, 2425226, 8578828, 30346157, 107344412, 379712753, 1343169821, 4751236703, 16806698494, 59450861306, 210297394895, 743891565706, 2631390949017, 9308101672049, 32925839761497

Offset

1,1

Comments

Column 3 of A212782.

Links

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

Formula

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

Empirical g.f.: x*(28 + 43*x + 12*x^2 - 41*x^3 - 32*x^4) / (1 - 2*x - 5*x^2 - 3*x^3 + 4*x^4 + 4*x^5). - Colin Barker, Jul 21 2018

Example

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

Crossrefs

Cf. A212782.

Sequence in context: A231230 A233375 A219691 * A130281 A255218 A168254

Adjacent sequences: A212774 A212775 A212776 * A212778 A212779 A212780

Keyword

nonn

Author

R. H. Hardin, May 27 2012

Status

approved