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URL: https://oeis.org/A190038

⇱ A190038 - OEIS

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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 04 2011
STATUS
approved