A166453 - OEIS

%I #9 Aug 08 2018 04:29:56

%S 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,

%T 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

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

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

%C Left border = A001316

%H E. Burlachenko, <a href="https://arxiv.org/abs/1612.00970">Fractal generalized Pascal matrices</a>, arXiv:1612.00970 [math.NT], 2016. See p. 13.

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

%e First few rows of the triangle =

%e 1;

%e 2, 1;

%e 2, 0, 1;

%e 4, 2, 2, 1;

%e 2, 0, 0, 0, 1;

%e 4, 2, 0, 0, 2, 1;

%e 4, 0, 2, 0, 2, 0, 1;

%e 8, 4, 4, 2, 4, 2, 2, 1;

%e 2, 0, 0, 0, 0, 0, 0, 0, 1;

%e 4, 2, 0, 0, 0, 0, 0, 0, 2, 1;

%e 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1;

%e 8, 4, 4, 2, 0, 0, 0, 0, 4, 2, 2, 1;

%e 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1;

%e ...

%t rows = 11;

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

%t T2 = T.T;

%t Table[T2[[i, j]], {i, 1, rows}, {j, 1, i}] // Flatten (* _Jean-François Alcover_, Aug 08 2018, after _Robert G. Wilson v_ *)

%Y A047999, A001316

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Oct 13 2009