A190038 Number of nondecreasing arrangements of n+2 numbers in 0..6 with the last equal to 6 and each after the second equal to the sum of one or two of the preceding three.

10, 18, 30, 47, 72, 107, 151, 203, 263, 331, 407, 491, 583, 683, 791, 907, 1031, 1163, 1303, 1451, 1607, 1771, 1943, 2123, 2311, 2507, 2711, 2923, 3143, 3371, 3607, 3851, 4103, 4363, 4631, 4907, 5191, 5483, 5783, 6091, 6407, 6731, 7063, 7403, 7751, 8107

Offset

1,1

Comments

Column 6 of A190041.

Links

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

Formula

Empirical: a(n) = 4*n^2 - 8*n + 11 for n>5.

Conjectures from Colin Barker, May 04 2018: (Start)

G.f.: x*(10 - 12*x + 6*x^2 + x^3 + 3*x^4 + 2*x^5 - x^6 - x^7) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

(End)

Example

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

Crossrefs

Cf. A190041.

Sequence in context: A256382 A167607 A162828 * A233695 A014006 A090995

Adjacent sequences: A190035 A190036 A190037 * A190039 A190040 A190041

Keyword

nonn

Author

R. H. Hardin, May 04 2011

Status

approved