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A166453 Triangle read by rows, square of Sierpinski's gasket, (A047999)^2.

%I A166453 #11 Jun 02 2025 02:09:14
%S A166453 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 A166453 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 A166453 Triangle read by rows, square of Sierpinski's gasket, (A047999)^2.
%C A166453 Row sums = A048883: (1, 3, 3, 9, 3, 9, 9, 27, 3, 9, 9, 27,...)
%C A166453 Left border = A001316
%H A166453 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 A166453 (A047999)^2, as an infinite lower triangular matrix.
%e A166453 First few rows of the triangle =
%e A166453 1;
%e A166453 2, 1;
%e A166453 2, 0, 1;
%e A166453 4, 2, 2, 1;
%e A166453 2, 0, 0, 0, 1;
%e A166453 4, 2, 0, 0, 2, 1;
%e A166453 4, 0, 2, 0, 2, 0, 1;
%e A166453 8, 4, 4, 2, 4, 2, 2, 1;
%e A166453 2, 0, 0, 0, 0, 0, 0, 0, 1;
%e A166453 4, 2, 0, 0, 0, 0, 0, 0, 2, 1;
%e A166453 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1;
%e A166453 8, 4, 4, 2, 0, 0, 0, 0, 4, 2, 2, 1;
%e A166453 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1;
%e A166453 ...
%t A166453 rows = 11;
%t A166453 T = PadRight[#, rows]& /@ Mod[NestList[Prepend[#, 0] + Append[#, 0]&, {1}, rows-1], 2];
%t A166453 T2 = T.T;
%t A166453 Table[T2[[i, j]], {i, 1, rows}, {j, 1, i}] // Flatten (* _Jean-François Alcover_, Aug 08 2018, after _Robert G. Wilson v_ *)
%Y A166453 A047999, A001316
%K A166453 nonn,tabl
%O A166453 0,2
%A A166453 _Gary W. Adamson_, Oct 13 2009