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
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Mar 26 2013
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Dec 27 2023
STATUS
approved