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A190040
Number of nondecreasing arrangements of n+2 numbers in 0..8 with the last equal to 8 and each after the second equal to the sum of one or two of the preceding three.
1
13, 24, 40, 65, 105, 164, 246, 349, 472, 617, 786, 981, 1204, 1457, 1742, 2061, 2416, 2809, 3242, 3717, 4236, 4801, 5414, 6077, 6792, 7561, 8386, 9269, 10212, 11217, 12286, 13421, 14624, 15897, 17242, 18661, 20156, 21729, 23382, 25117, 26936, 28841
OFFSET
1,1
COMMENTS
Column 8 of A190041.
LINKS
FORMULA
Empirical: a(n) = (1/3)*n^3 + 2*n^2 + (50/3)*n - 83 for n>6.
Conjectures from Colin Barker, May 04 2018: (Start)
G.f.: x*(13 - 28*x + 22*x^2 - 3*x^3 + 2*x^4 - 2*x^5 - 6*x^7 + x^8 + 3*x^9) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.
(End)
EXAMPLE
Some solutions for n=3:
..1....2....6....0....0....0....1....2....3....2....1....2....8....3....2....1
..4....4....8....8....4....4....4....4....8....6....4....6....8....4....3....7
..4....4....8....8....4....4....4....4....8....6....4....8....8....4....5....8
..8....4....8....8....4....8....5....8....8....8....4....8....8....4....8....8
..8....8....8....8....8....8....8....8....8....8....8....8....8....8....8....8
CROSSREFS
Cf. A190041.
Sequence in context: A363823 A032607 A335973 * A081723 A189325 A053080
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 04 2011
STATUS
approved