A190035 Number of nondecreasing arrangements of n+2 numbers in 0..3 with the last equal to 3 and each after the second equal to the sum of one or two of the preceding three.

5, 7, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202, 206, 210, 214, 218, 222, 226, 230, 234, 238

Offset

1,1

Comments

Column 3 of A190041.

Links

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

Formula

Empirical: a(n) = 4*n - 2 for n>2.

Conjectures from Colin Barker, May 03 2018: (Start)

G.f.: x*(5 - 3*x + x^2 + x^3) / (1 - x)^2.

a(n) = 2*a(n-1) - a(n-2) for n>4.

(End)

Example

All solutions for n=4:
..1....1....0....3....2....0....1....0....1....1....0....1....1....1
..1....1....3....3....3....1....1....1....2....1....1....2....3....1
..2....1....3....3....3....1....2....1....3....1....1....2....3....1
..2....1....3....3....3....2....3....2....3....2....1....3....3....2
..3....2....3....3....3....2....3....3....3....3....2....3....3....2
..3....3....3....3....3....3....3....3....3....3....3....3....3....3

Crossrefs

Cf. A190041.

Sequence in context: A022441 A156243 A020942 * A071911 A070875 A091522

Adjacent sequences: A190032 A190033 A190034 * A190036 A190037 A190038

Keyword

nonn

Author

R. H. Hardin, May 04 2011

Status

approved