A337266 Array read by antidiagonals: T(m,n) (m>=0, n>=0) = number of paths to origin (0,0) from grid point (m,n) in the Even Conant lattice.

1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 4, 2, 1, 1, 1, 5, 2, 1, 1, 1, 2, 6, 2, 1, 2, 1, 1, 3, 0, 8, 3, 3, 1, 1, 1, 1, 3, 0, 11, 0, 4, 2, 1, 1, 1, 1, 3, 11, 0, 4, 2, 1, 1, 1, 2, 1, 4, 14, 11, 4, 6, 1, 2, 1

Offset

0,5

Comments

The paths only use steps to the left and downwards.

Links

Table of n, a(n) for n=0..65.

N. J. A. Sloane, Notes on the Conant Gasket, the Conant Lattice, and Associated Sequences, Preliminary version, Aug 23 2020

N. J. A. Sloane, The Even Conant Lattice (The grid points (m,n) are labeled with pairs v(m,n), h(m,n).)

N. J. A. Sloane, Portion of the Even Conant Lattice, with number of paths to origin shown in red.

Formula

T(m,n) = v(m,n-1)*T(m,n-1)+h(m-1,n)*T(m-1,n), where v = A337263, h = A337264.

Example

The initial antidiagonals (starting in the bottom left corner) are:
1,
1,1,
1,2,1,
1,3,1,1,
1,1,4,2,1,
1,1,5,2,1,1,
1,2,6,2,1,2,1,
1,3,0,8,3,3,1,1,
1,1,3,0,11,0,4,2,1,
1,1,1,3,11,0,4,2,1,1,
1,2,1,4,14,11,4,6,1,2,1,
...

Crossrefs

Cf. A328078, A328080, A337263, A337264, A337265.

Sequence in context: A106177 A211985 A211009 * A211986 A211989 A207377

Adjacent sequences: A337263 A337264 A337265 * A337267 A337268 A337269

Keyword

nonn,tabl

Author

N. J. A. Sloane, Aug 22 2020

Status

approved