cp's OEIS Frontend

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.)

%I A047130 #14 Jan 20 2020 09:20:47
%S A047130 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,
%T A047130 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,
%U A047130 104,84,76,75,35,9,1,1,10,44,110,179,188,84
%N 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.)
%H A047130 Andrew Howroyd, <a href="/A047130/b047130.txt">Table of n, a(n) for n = 0..1325</a>
%e A047130 Array begins:
%e A047130 ===================================
%e A047130 h\k | 0 1  2  3   4   5   6   7
%e A047130 ----+------------------------------
%e A047130   0 | 1 1  1  1   1   1   1   1 ...
%e A047130   1 | 1 1  2  3   4   5   6   7 ...
%e A047130   2 | 1 2  2  5   9  14  20  27 ...
%e A047130   3 | 1 3  5  5  14  28  48  75 ...
%e A047130   4 | 1 4  9 14  28  56 104 179 ...
%e A047130   5 | 1 5 14 28  28  84 188 367 ...
%e A047130   6 | 1 6 20 48  76  84 272 639 ...
%e A047130   7 | 1 7 27 75 151 235 272 911 ...
%e A047130   ...
%o A047130 (PARI)
%o A047130 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}
%o A047130 { my(T=A(10)); for(i=1, #T, print(T[i, ]))} \\ _Andrew Howroyd_, Jan 19 2020
%Y A047130 Cf. A047131, A047132, A047133, A047134, A047135, A047136, A047137, A047138, A047139.
%Y A047130 Cf. A047110, A047140, A047150.
%K A047130 nonn,tabl
%O A047130 0,8
%A A047130 _Clark Kimberling_. Definition revised Dec 08 2006