A248462 Number of length 1+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

6, 18, 48, 96, 174, 282, 432, 624, 870, 1170, 1536, 1968, 2478, 3066, 3744, 4512, 5382, 6354, 7440, 8640, 9966, 11418, 13008, 14736, 16614, 18642, 20832, 23184, 25710, 28410, 31296, 34368, 37638, 41106, 44784, 48672, 52782, 57114, 61680, 66480, 71526

Offset

1,1

Links

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

Formula

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

Empirical for n mod 12 = 0: a(n) = n^3 + (3/2)*n^2 + 2*n.

Empirical for n mod 12 = 1: a(n) = n^3 + (3/2)*n^2 + 2*n + (3/2).

Empirical g.f.: 6*x*(1 + x^2) / ((1 - x)^4*(1 + x)). - Colin Barker, Nov 08 2018

Example

Some solutions for n=6:
..2....1....4....6....5....3....0....5....4....4....0....6....0....4....4....2
..1....5....4....1....6....4....1....5....2....1....6....3....6....2....6....5
..4....2....0....1....0....1....3....6....5....4....4....6....6....2....1....3

Crossrefs

Row 1 of A248461.

Sequence in context: A328890 A188379 A299268 * A256010 A128543 A003202

Adjacent sequences: A248459 A248460 A248461 * A248463 A248464 A248465

Keyword

nonn

Author

R. H. Hardin, Oct 06 2014

Status

approved