A256369 Number of triangular 0..1 arrays with n rows such that the k-th row of the array (with the first row of the triangle indexed with 0) has 2*k+1 elements and row sums are nondecreasing from top to bottom.

2, 15, 406, 40258, 14831678, 20517694389, 107429900933236, 2142202276884870716, 163481473873315612871890, 47938888004647069685675105423, 54195408755986948204810401084145420, 236870277534533345162432986910962427358196

Offset

1,1

Comments

The number of binary strings of length a with exactly x ones (or zeros) is binomial(a, x).

Links

Lars Blomberg, Table of n, a(n) for n = 1..58

Formula

a(n) = Sum_{i_0=0..1} ... Sum_{i_k=i_(k-1)..2k+1} ... Sum_{i_(n-1)=i_(n-2)..2n-1} Product_{k=0..n-1} binomial(2k+1,i_k). - Danny Rorabaugh, Mar 31 2015

Example

a(2) = binomial(3, 0) + binomial(3, 1)*2 + binomial(3, 2)*2 + binomial(3, 3)*2 = 15.
Some eligible arrays for n=2:
...0......0......0......0......0......0......0......0......1......1...
.0.0.0..1.0.0..0.1.0..0.0.1..1.1.0..1.0.1..0.1.1..1.1.1..1.0.0..0.1.0.
Some eligible arrays for n=3:
.....0..........0..........0..........0..........0..........0.....
...0.0.0......0.0.0......0.0.0......0.0.0......0.0.0......0.0.0...
.0.0.0.0.0..1.0.0.0.0..0.1.0.0.0..0.0.1.0.0..0.0.0.1.0..0.0.0.0.1.

Crossrefs

Sequence in context: A071102 A272899 A060381 * A145328 A139810 A012943

Adjacent sequences: A256366 A256367 A256368 * A256370 A256371 A256372

Keyword

nonn

Author

Felix Fröhlich, Mar 26 2015

Extensions

a(4)-a(12) from Lars Blomberg, Apr 11 2015

Status

approved