

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 xaxis, no paths begin with W, all W steps remain on the xaxis 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
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OFFSET

0,4


COMMENTS

The row sums are the evenindexed Fibonacci numbers.


REFERENCES

A. Nkwanta, A Riordan matrix approach to unifying a selected class of combinatorial arrays, Congressus Numerantium, 160 (2003), pp. 3355.
A. Nkwanta, A note on Riordan matrices, Contemporary Mathematics Series, AMS, 252 (1999), pp. 99107.
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(nj, j)j>=1, n>=1 for leftmost column and d(n+1, k) = d(n, k1) + d(n, k) + sum(d(nj, k+j)j>=1, n>=2, k>=1 and n>j; Riordan array d(n, k): (((1z)/2z)*(sqrt(1+z+z^2)/sqrt(13z+z^2) 1), ((1z+z^2)sqrt(12zz^22z^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



