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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.). 11
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, 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, 38, 142, 148, 102, 43, 10, 1, 1, 9, 35, 85, 96, 180, 290 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
EXAMPLE
Array begins:
======================================
h\k | 0 1 2 3 4 5 6 7
----+---------------------------------
0 | 1 1 1 1 1 1 1 1 ...
1 | 1 2 1 2 3 4 5 6 ...
2 | 1 3 4 2 5 9 14 20 ...
3 | 1 4 8 10 15 24 38 58 ...
4 | 1 5 13 23 38 62 38 96 ...
5 | 1 6 19 42 80 142 180 96 ...
6 | 1 7 26 68 148 290 470 566 ...
7 | 1 8 34 102 250 540 1010 1576 ...
...
PROG
(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}
{ my(T=A(10)); for(i=1, #T, print(T[i, ]))} \\ Andrew Howroyd, Jan 19 2020
CROSSREFS
Sequence in context: A111603 A180178 A136178 * A047150 A280489 A289356
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling. Definition revised Dec 08 2006
STATUS
approved

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Last modified April 19 07:24 EDT 2024. Contains 371782 sequences. (Running on oeis4.)