0,4

The Delannoy triangle is A008288 viewed as a number triangle. It is then given by the Riordan array (1/(1-x), x(1+x)/(1-x)). The absolute value of A103136 is the Riordan array (1+xS(x),xS(x)) which is the inverse of the signed Delannoy triangle (1/(1+x), x(1-x)/(1+x)).

Triangle T(n,k), 0<=k<=n, read by rows, given by : [ -1, -1, -2, -1, -2, -1, -2, -1, -2, ... ] DELTA [ 1, 0, 0, 0, 0, 0, 0, 0, ... ] where DELTA is the operator defined in A084938; the unsigned version is given by [ 1, 1, 2, 1, 2, 1, 2, 1, 2, ...] DELTA [ 1, 0, 0, 0, 0, 0, 0, 0, ... ] . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 08 2005

The unsigned number |T(n,k)| counts Schroeder n-paths whose ascent starting at the initial vertex has length k. A Schroeder n-path is a lattice path starting from (0,0), ending at (2n,0), consisting only of steps U=(1,1) (upsteps), D=(1,-1) (downsteps) and F=(2,0) (flatsteps) and never going below the x-axis. For example, |T(2,0)| = 2 counts FF, FUD; |T(2,1)| = 3 counts UFD, UDF, UDUD; |T(2,2)| = 1 counts UUDD. - David Callan (callan(AT)stat.wisc.edu), Jul 14 2006

Riordan array (1-f(x), f(x)) with f(x)=xS(-x), S(x) the g.f. of the large Schroeder numbers A006318. Equivalent to Riordan array (g(x), 1-g(x)) where g(x)=(3+x-sqrt(1+6x+x^2))/2.

Sequence in context: A086211 A110189 A132372 this_sequence A086960 A138771 A121748

Adjacent sequences: A103133 A103134 A103135 this_sequence A103137 A103138 A103139

easy,sign,tabl

Paul Barry (pbarry(AT)wit.ie), Jan 24 2005