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A223718 Number of unimodal functions [1..n]->[0..2]. 23
1, 3, 9, 22, 46, 86, 148, 239, 367, 541, 771, 1068, 1444, 1912, 2486, 3181, 4013, 4999, 6157, 7506, 9066, 10858, 12904, 15227, 17851, 20801, 24103, 27784, 31872, 36396, 41386, 46873, 52889, 59467, 66641, 74446, 82918, 92094, 102012, 112711, 124231 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Column 1 of A223725.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n=1..210 from R. H. Hardin)
Kyu-Hwan Lee and Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016.
FORMULA
a(n) = A071920(n,3) = 1+n*(n+1)*(n^2+5*n+18)/24.
G.f.: 1-x*(x^2-3*x+3)*(x^2-x+1) / (x-1)^5 . a(n) = 1+A051744(n). - R. J. Mathar, May 17 2014
EXAMPLE
Some solutions for n=3
..1....2....0....1....0....2....1....2....0....2....0....1....0....1....0....1
..2....1....1....1....0....0....0....1....0....2....2....1....1....2....2....2
..0....1....0....0....1....0....0....0....2....2....1....1....1....2....0....1
From Joerg Arndt, Dec 27 2023: (Start)
The a(3) = 22 such functions are (dots for zeros)
1: [ . . . ]
2: [ . . 1 ]
3: [ . . 2 ]
4: [ . 1 . ]
5: [ . 1 1 ]
6: [ . 1 2 ]
7: [ . 2 . ]
8: [ . 2 1 ]
9: [ . 2 2 ]
10: [ 1 . . ]
11: [ 1 1 . ]
12: [ 1 1 1 ]
13: [ 1 1 2 ]
14: [ 1 2 . ]
15: [ 1 2 1 ]
16: [ 1 2 2 ]
17: [ 2 . . ]
18: [ 2 1 . ]
19: [ 2 1 1 ]
20: [ 2 2 . ]
21: [ 2 2 1 ]
22: [ 2 2 2 ]
(End)
CROSSREFS
Column m=3 of A071920.
Cf. A000124 (unimodal functions [1..n]->[0..1]), A088536 ([1..n] -> [1..n]).
Sequence in context: A131477 A002128 A064808 * A217882 A217881 A217880
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Mar 26 2013
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Dec 27 2023
STATUS
approved

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Last modified February 29 04:26 EST 2024. Contains 370401 sequences. (Running on oeis4.)