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%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
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