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A130123 Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the term 2^k. Triangle by columns, (2^k, 0, 0, 0,...). 8
1, 0, 2, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2048, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4096 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A 2^n transform matrix.

A130123 * A007318 = A038208. A007318 * A130123 = A013609. A130124 = A130123 * A002260. A130125 = A128174 * A130123.

Triangle T(n,k), 0<=k<=n, given by [0,0,0,0,0,0,...] DELTA [2,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . - Philippe Deléham, May 26 2007

Also the Bell transform of A000038. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 27 2016

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

FORMULA

G.f.: 1/(1-2*x*y). - R. J. Mathar, Aug 11 2015

EXAMPLE

First few terms of the triangle are:

  1;

  0, 2;

  0, 0, 4;

  0, 0, 0, 8;

  0, 0, 0, 0, 16;

  0, 0, 0, 0, 0, 32; ...

MAPLE

# The function BellMatrix is defined in A264428.

BellMatrix(n -> `if`(n=0, 2, 0), 9); # Peter Luschny, Jan 27 2016

MATHEMATICA

BellMatrix[f_Function, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];

rows = 12;

M = BellMatrix[If[# == 0, 2, 0]&, rows];

Table[M[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 23 2018, after Peter Luschny *)

Table[If[k==n, 2^n, 0], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jun 05 2019 *)

PROG

(PARI) {T(n, k) = if(k==n, 2^n, 0)}; \\ G. C. Greubel, Jun 05 2019

(MAGMA) [[k eq n select 2^n else 0: k in [0..n]]: n in [0..14]]; // G. C. Greubel, Jun 05 2019

(Sage)

def T(n, k):

    if (k==n): return 2^n

    else: return 0

[[T(n, k) for k in (0..n)] for n in (0..14)] # G. C. Greubel, Jun 05 2019

CROSSREFS

Cf. A130124, A130125.

Sequence in context: A028590 A074644 A321256 * A319935 A136337 A028601

Adjacent sequences:  A130120 A130121 A130122 * A130124 A130125 A130126

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, May 11 2007

STATUS

approved

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Last modified December 14 03:31 EST 2019. Contains 329978 sequences. (Running on oeis4.)