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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

Table of n, a(n) for n=0..54.

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: A184050 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 January 18 03:13 EST 2019. Contains 319260 sequences. (Running on oeis4.)