A227924 Triangle T(n,k): the number of binary sequences of n zeros and n ones in which the shortest run is of length k.

2, 4, 2, 18, 0, 2, 64, 4, 0, 2, 238, 12, 0, 0, 2, 890, 28, 4, 0, 0, 2, 3348, 70, 12, 0, 0, 0, 2, 12662, 182, 20, 4, 0, 0, 0, 2, 48102, 466, 38, 12, 0, 0, 0, 0, 2, 183460, 1186, 84, 20, 4, 0, 0, 0, 0, 2

Offset

1,1

Comments

Row n sums to C(2n,n) (A000984).

Links

Andrew Woods, Rows n = 1..50 of triangle, flattened

Example

The triangle begins:
[2,
[4,   2,
[18,  0,  2,
[64,  4,  0, 2,
[238, 12, 0, 0, 2,
The second row counts the sets {0101, 1010, 0110, 1001} and {0011, 1100}.

Prog

(PARI)
bn(n, k)=binomial(max(0, n), k)
f(n, k)=2*sum(x=1, floor(n/k), bn(n+x*(1-k)-1, x-1)*(bn(n+x*(1-k)-1, x-1)+bn(n+(x+1)*(1-k)-1, x)))
T(n, k)=f(n, k)-f(n, k+1)
r(n)=vector(n, x, T(n, x))

Crossrefs

Cf. A229756.

Sequence in context: A186526 A350816 A326723 * A100944 A295390 A059890

Adjacent sequences: A227921 A227922 A227923 * A227925 A227926 A227927

Keyword

nonn,tabl

Author

Andrew Woods, Oct 09 2013

Status

approved