A047010 - OEIS

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.

%I #11 Jan 24 2018 01:02:59

%S 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,

%T 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,

%U 120,111,61,15,9,6,1,1,10,45,119,203,231,172,76,15

%N 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.

%H M. Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv preprint arXiv:1301.4550, 2013. - From N. J. A. Sloane, Feb 13 2013

%H M. Janjic, B. Petkovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Janjic/janjic45.html">A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers</a>, J. Int. Seq. 17 (2014) # 14.3.5

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

%K nonn,tabl

%O 0,8

%A _Clark Kimberling_