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A190036
Number of nondecreasing arrangements of n+2 numbers in 0..4 with the last equal to 4 and each after the second equal to the sum of one or two of the preceding three.
1
7, 12, 18, 27, 39, 53, 69, 87, 107, 129, 153, 179, 207, 237, 269, 303, 339, 377, 417, 459, 503, 549, 597, 647, 699, 753, 809, 867, 927, 989, 1053, 1119, 1187, 1257, 1329, 1403, 1479, 1557, 1637, 1719, 1803, 1889, 1977, 2067, 2159, 2253, 2349, 2447, 2547, 2649
OFFSET
1,1
COMMENTS
Column 4 of A190041.
LINKS
FORMULA
Empirical: a(n) = n^2 + 3*n - 1 for n>3.
Conjectures from Colin Barker, May 04 2018: (Start)
G.f.: x*(7 - 9*x + 3*x^2 + 2*x^3 - x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
(End)
EXAMPLE
Some solutions for n=3:
2 1 1 3 1 2 0 1 0 1 1 2 0 1 1 4
2 1 1 4 4 2 2 2 2 3 2 2 4 2 3 4
4 2 2 4 4 2 2 2 2 3 2 2 4 3 4 4
4 2 3 4 4 4 2 2 4 4 4 2 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
CROSSREFS
Cf. A190041.
Sequence in context: A247159 A022953 A030714 * A061141 A256381 A272975
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 04 2011
STATUS
approved