A047130 Array read by descending antidiagonals: T(h,k) is the 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 = 3x/4. (Thus a path crosses the line only at lattice points and on right-steps.)
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 4, 5, 5, 4, 1, 1, 5, 9, 5, 9, 5, 1, 1, 6, 14, 14, 14, 14, 6, 1, 1, 7, 20, 28, 28, 28, 20, 7, 1, 1, 8, 27, 48, 56, 28, 48, 27, 8, 1, 1, 9, 35, 75, 104, 84, 76, 75, 35, 9, 1, 1, 10, 44, 110, 179, 188, 84
Offset: 0
Examples
Array begins: =================================== h\k | 0 1 2 3 4 5 6 7 ----+------------------------------ 0 | 1 1 1 1 1 1 1 1 ... 1 | 1 1 2 3 4 5 6 7 ... 2 | 1 2 2 5 9 14 20 27 ... 3 | 1 3 5 5 14 28 48 75 ... 4 | 1 4 9 14 28 56 104 179 ... 5 | 1 5 14 28 28 84 188 367 ... 6 | 1 6 20 48 76 84 272 639 ... 7 | 1 7 27 75 151 235 272 911 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325
Crossrefs
Programs
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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(4*k>3*h && 4*(k-1)<3*h, 0, M[1+h, k]))); M} { my(T=A(10)); for(i=1, #T, print(T[i, ]))} \\ Andrew Howroyd, Jan 19 2020