A166453 - OEIS

A166453

Triangle read by rows, square of Sierpinski's gasket, (A047999)^2

1, 2, 1, 2, 0, 1, 4, 2, 2, 1, 2, 0, 0, 0, 1, 4, 2, 0, 0, 2, 1, 4, 0, 2, 0, 2, 0, 1, 8, 4, 4, 2, 4, 2, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 4, 2, 0, 0, 0, 0, 0, 0, 2, 1, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Row sums = A048883: (1, 3, 3, 9, 3, 9, 9, 27, 3, 9, 9, 27,...)

Left border = A001316

LINKS

Table of n, a(n) for n=0..65.

E. Burlachenko, Fractal generalized Pascal matrices, arXiv:1612.00970 [math.NT], 2016. See p. 13.

FORMULA

(A047999)^2, as an infinite lower triangular matrix.

EXAMPLE

First few rows of the triangle =

2, 1;

2, 0, 1;

4, 2, 2, 1;

2, 0, 0, 0, 1;

4, 2, 0, 0, 2, 1;

4, 0, 2, 0, 2, 0, 1;

8, 4, 4, 2, 4, 2, 2, 1;

2, 0, 0, 0, 0, 0, 0, 0, 1;

4, 2, 0, 0, 0, 0, 0, 0, 2, 1;

4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1;

8, 4, 4, 2, 0, 0, 0, 0, 4, 2, 2, 1;

4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1;

...

MATHEMATICA

rows = 11;

T = PadRight[#, rows]& /@ Mod[NestList[Prepend[#, 0] + Append[#, 0]&, {1}, rows-1], 2];

T2 = T.T;

Table[T2[[i, j]], {i, 1, rows}, {j, 1, i}] // Flatten (* Jean-François Alcover, Aug 08 2018, after Robert G. Wilson v *)

CROSSREFS

A047999, A001316

Sequence in context: A129559 A129680 A118231 * A118233 A255273 A181117

Adjacent sequences: A166450 A166451 A166452 * A166454 A166455 A166456

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Oct 13 2009

STATUS

approved