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 A165191 Irregular triangle B(n,i) = i-th significant bit of Gray code of n. 0
 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 COMMENTS The n-th row has length A070939(n); a nondecreasing sequence. Each row, when interpreted as a finite sequence can be mapped via Euler's Transform to familiar integer sequences. Note that adjacent rows differ by only one "bit" which simplifies the transition from one row to the next. (cf. A003188, A055975 and A119972). LINKS FORMULA The n-th row is the reversed bit string of A003188(n). Namely, A003188(n) = Sum_{0<=ix+y, [B(2^(b+1)-1-n)], [0\$b, 1], 0)[])     end: seq(B(n), n=0..30);  # Alois P. Heinz, May 21 2012 MATHEMATICA zip = With[{m = Max[Length[#1], Length[#2]]}, PadRight[#1, m] + PadRight[#2, m]]&; B[n_] := B[n] = With[{b = Floor[Log[2, n]]}, If[n <= 1, {n}, zip[B[2^(b+1)-1-n], Append[Array[0&, b], 1]]]]; Table[B[n], {n, 0, 30}] // Flatten (* Jean-François Alcover, Feb 13 2017, after Alois P. Heinz *) PROG (MAGMA) // Recursive N := 5; s := [[]]; for n in [1..N] do   for j in [#s..1 by -1] do     Append(~s, Append(s[j], 1));     Append(~s[j], 0);   end for; end for; &cat[IntegerToSequence(SequenceToInteger(b, 2), 2):b in s]; (MAGMA) // Direct B:=func; CROSSREFS Euler transforms of the rows begin: A000007, A000012, A008619, A059841, A103221, A001399, A008620, A022003, A008679, A025767, A001400. Sequence in context: A168395 A278718 A130854 * A189576 A112448 A101264 Adjacent sequences:  A165188 A165189 A165190 * A165192 A165193 A165194 KEYWORD nonn,easy,tabf AUTHOR Alford Arnold, Sep 29 2009 EXTENSIONS Edited by Jason Kimberley, Mar 31 2012 STATUS approved

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Last modified June 14 13:23 EDT 2021. Contains 345025 sequences. (Running on oeis4.)