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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
2, 15, 406, 40258, 14831678, 20517694389, 107429900933236, 2142202276884870716, 163481473873315612871890, 47938888004647069685675105423, 54195408755986948204810401084145420, 236870277534533345162432986910962427358196 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 16 19:15 EDT 2021. Contains 343951 sequences. (Running on oeis4.)