cp's OEIS Frontend

A047140 Array 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 up-step crosses the line y=4x/3. (Thus a path crosses the line only at lattice points and on right-steps.).

%I A047140 #11 Jan 19 2020 20:38:41
%S A047140 1,1,1,1,2,1,1,1,3,1,1,2,4,4,1,1,3,2,8,5,1,1,4,5,10,13,6,1,1,5,9,15,
%T A047140 23,19,7,1,1,6,14,24,38,42,26,8,1,1,7,20,38,62,80,68,34,9,1,1,8,27,58,
%U A047140 38,142,148,102,43,10,1,1,9,35,85,96,180,290
%N A047140 Array 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 up-step crosses the line y=4x/3. (Thus a path crosses the line only at lattice points and on right-steps.).
%H A047140 Andrew Howroyd, <a href="/A047140/b047140.txt">Table of n, a(n) for n = 0..1325</a>
%e A047140 Array begins:
%e A047140 ======================================
%e A047140 h\k | 0 1  2   3   4   5    6    7
%e A047140 ----+---------------------------------
%e A047140   0 | 1 1  1   1   1   1    1    1 ...
%e A047140   1 | 1 2  1   2   3   4    5    6 ...
%e A047140   2 | 1 3  4   2   5   9   14   20 ...
%e A047140   3 | 1 4  8  10  15  24   38   58 ...
%e A047140   4 | 1 5 13  23  38  62   38   96 ...
%e A047140   5 | 1 6 19  42  80 142  180   96 ...
%e A047140   6 | 1 7 26  68 148 290  470  566 ...
%e A047140   7 | 1 8 34 102 250 540 1010 1576 ...
%e A047140   ...
%o A047140 (PARI) A(h,k=h)={my(M=matrix(h+1,k+1,i,j,1)); for(h=1, h, for(k=1, k, M[1+h, 1+k] = M[h,1+k] + if(3*k>4*h && 3*(k-1)<4*h, 0, M[1+h,k]))); M}
%o A047140 { my(T=A(10)); for(i=1, #T, print(T[i,]))} \\ _Andrew Howroyd_, Jan 19 2020
%Y A047140 Cf. A047141, A047142, A047143, A047144, A047145, A047146, A047147, A047148, A047149.
%Y A047140 Cf. A047110, A047130, A047150.
%K A047140 nonn,tabl
%O A047140 0,5
%A A047140 _Clark Kimberling_. Definition revised Dec 08 2006