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 A110438 Triangular array giving the number of NSEW unit step lattice paths of length n with terminal height k subject to the following restrictions. The paths start at the origin (0,0) and take unit steps (0,1)=N(north), (0,-1)=S(south), (1,0)=E(east) and (-1,0)=W(west) such that no paths pass below the x-axis, no paths begin with W, all W steps remain on the x-axis and there are no NS steps. 0
 1, 1, 1, 2, 2, 1, 5, 4, 3, 1, 12, 10, 7, 4, 1, 29, 25, 18, 11, 5, 1, 71, 62, 47, 30, 16, 6, 1, 175, 155, 121, 82, 47, 22, 7, 1, 434, 389, 311, 220, 135, 70, 29, 8, 1, 1082, 979, 799, 584, 378, 212, 100, 37, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The row sums are the even-indexed Fibonacci numbers. REFERENCES A. Nkwanta, A Riordan matrix approach to unifying a selected class of combinatorial arrays, Congressus Numerantium, 160 (2003), pp. 33-55. A. Nkwanta, A note on Riordan matrices, Contemporary Mathematics Series, AMS, 252 (1999), pp. 99-107. A. Nkwanta, Lattice paths, generating functions and the Riordan group, Ph.D. Thesis, Howard University, Washington DC, 1997. LINKS Naiomi T. Cameron and Asamoah Nkwanta, On Some (Pseudo) Involutions in the Riordan Group, Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.7. FORMULA Recurrence is d(0, 0)= 1, d(1, 0)=1, d(n+1, 0) = 2*d(n, 0) + sum(d(n-j, j)j>=1, n>=1 for leftmost column and d(n+1, k) = d(n, k-1) + d(n, k) + sum(d(n-j, k+j)j>=1, n>=2, k>=1 and n>j; Riordan array d(n, k): (((1-z)/2z)*(sqrt(1+z+z^2)/sqrt(1-3z+z^2) -1), ((1-z+z^2)-sqrt(1-2z-z^2-2z^3+z^4)/2z)). EXAMPLE Triangle starts: 1; 1,1; 2,2,1; 5,4,3,1; 12,10,7,4,1; CROSSREFS Cf. A097724. Sequence in context: A324798 A226059 A127742 * A184051 A121460 A105292 Adjacent sequences:  A110435 A110436 A110437 * A110439 A110440 A110441 KEYWORD easy,nonn,tabl AUTHOR Asamoah Nkwanta (Nkwanta(AT)jewel.morgan.edu), Aug 10 2005 STATUS approved

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Last modified October 14 14:45 EDT 2019. Contains 328019 sequences. (Running on oeis4.)