A049695 Array T read by diagonals; T(i,j) is the number of nonnegative slopes of lines determined by 2 lattice points in [ 0,i ] X [ 0,j ] if i > 0; T(0,j)=1 if j > 0; T(0,0)=0.

0, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 4, 4, 1, 1, 5, 6, 6, 5, 1, 1, 6, 7, 8, 7, 6, 1, 1, 7, 9, 10, 10, 9, 7, 1, 1, 8, 10, 13, 12, 13, 10, 8, 1, 1, 9, 12, 14, 16, 16, 14, 12, 9, 1, 1, 10, 13, 17, 17, 20, 17, 17, 13, 10, 1, 1, 11, 15, 19, 21, 22, 22, 21, 19, 15, 11, 1, 1, 12, 16, 21, 23, 27, 24, 27

Offset

0,5

Comments

The infinity slope is not counted unless i=0 and j>0. - Max Alekseyev, Oct 23 2008

Links

Table of n, a(n) for n=0..85.

Max A. Alekseyev. On the number of two-dimensional threshold functions, arXiv:math/0602511 [math.CO], 2006-2010; SIAM J. Disc. Math. 24(4), 2010, pp. 1617-1631. doi:10.1137/090750184.

Formula

For m,n > 0, T(m,n) = 1 + U(m,n) = 1 + Sum_{i=1..m, j=1..n, gcd(i,j)=1} 1. - Max Alekseyev, Oct 23 2008

Example

Diagonals (each starting on row 1): {0}; {1,1}; {1,2,1}; ...

Crossrefs

Cf. A005598, A049703, A114043.

Sequence in context: A116188 A318274 A329330 * A096589 A176427 A324592

Adjacent sequences: A049692 A049693 A049694 * A049696 A049697 A049698

Keyword

nonn,tabl,easy

Author

Clark Kimberling

Extensions

More terms from Max Alekseyev, Oct 23 2008

Status

approved