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A129186
Right shift operator generating 1's in shifted spaces.
20
1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0,1
COMMENTS
LetA129186= M, then M*V, V a vector; shifts V to the right, appending 1's to the shifted spaces. Example: M*V, V = [1,2,3,...] = [1,1,2,3,...].
Triangle T(n,k), read by rows, given by (1, -1, 0, 0, 0, 0, 0, 0, 0,...) DELTA (0, 1, 0, 0, 0, 0, 0, 0, 0,...) where DELTA is the operator defined inA084938.-Philippe Deléham,Dec 08 2011
FORMULA
Infinite lower triangular matrix with (1,0,0,...) in the main diagonal and (1,1,1...) in the subdiagonal.
G.f.: (1-(y-1)*x)/(1-y*x). -Philippe Deléham,Dec 08 2011
EXAMPLE
First few rows of the triangle are:
1;
1, 0;
0, 1, 0;
0, 0, 1, 0;
0, 0, 0, 1, 0;
...
MAPLE
gf:= 1 + z/(1 - x*z): ser:= series(gf, z, 16): c:= k -> coeff(ser, z, k):
seq(seq(coeff(c(n), x, k), k=0..n), n=0..14); #Peter Luschny,Jul 07 2019
MATHEMATICA
Join[{1}, Flatten[Table[PadLeft[{1, 0}, n, 0], {n, 2, 20}]]] (*Harvey P. Dale,Aug 26 2019 *)
CROSSREFS
Generalized Eulerian triangles: this sequence (m=0),A173018(m=1),A292604(m=2).
KEYWORD
nonn,easy,tabl
AUTHOR
Gary W. Adamson,Apr 01 2007
STATUS
approved