A129186 Right shift operator generating 1's in shifted spaces.

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

Let A129186 = 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 in A084938. - Philippe Deléham, Dec 08 2011

Links

Robert Price, Table of n, a(n) for n = 0..5049

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).

Cf. A000012 (row sums), A071919, A129184, A129185.

Sequence in context: A039985 A324822 A127239 * A353494 A190610 A095901

Adjacent sequences: A129183 A129184 A129185 * A129187 A129188 A129189

Keyword

nonn,easy,tabl

Author

Gary W. Adamson, Apr 01 2007

Status

approved