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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.
2
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
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
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Aug 22 2020
STATUS
approved