A047010 Array T read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and no step touches the line y=x/3 unless x=0 or x=h.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 2, 1, 1, 4, 6, 3, 1, 1, 1, 5, 10, 9, 3, 2, 1, 1, 6, 15, 19, 12, 3, 3, 1, 1, 7, 21, 34, 31, 15, 6, 4, 1, 1, 8, 28, 55, 65, 46, 15, 4, 5, 1, 1, 9, 36, 83, 120, 111, 61, 15, 9, 6, 1, 1, 10, 45, 119, 203, 231, 172, 76, 15

Offset

0,8

Links

Table of n, a(n) for n=0..74.

M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550, 2013. - From N. J. A. Sloane, Feb 13 2013

M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5

Example

Diagonals (beginning on row 0): {1}; {1,1}; {1,1,1}; {1,2,1,1}; {1,3,3,2,1}; ...

Crossrefs

Sequence in context: A180303 A118923 A292745 * A047100 A124772 A227543

Adjacent sequences: A047007 A047008 A047009 * A047011 A047012 A047013

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved