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A272188 Triangle with 2*n+1 terms per row, read by rows: the first row is 1 (by decree), following rows contain 0 to 2n+1 but omitting 2n.

%I A272188 #20 Apr 29 2016 09:20:00
%S A272188 1,0,1,3,0,1,2,3,5,0,1,2,3,4,5,7,0,1,2,3,4,5,6,7,9,0,1,2,3,4,5,6,7,8,
%T A272188 9,11,0,1,2,3,4,5,6,7,8,9,10,11,13,0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,
%U A272188 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17
%N A272188 Triangle with 2*n+1 terms per row, read by rows: the first row is 1 (by decree), following rows contain 0 to 2n+1 but omitting 2n.
%C A272188 Row n is row 2n+1 of A128138, a bisection.
%C A272188 The second bisection by rows
%C A272188 0, 2,
%C A272188 0, 1, 2, 4,
%C A272188 0, 1, 2, 3, 4, 6,
%C A272188 0, 1, 2, 3, 4, 5, 6, 8,
%C A272188 etc
%C A272188 is the basis of
%C A272188 0, 2, 4, 6, 8, 10, 12, ... the even numbers A005843(n)
%C A272188 0, 1, 2, 4, 3,  6,  8, 5, 10, ... a permutation of the nonnegative integers A265667(n).
%C A272188 0, 1, 2, 3, 4,  6,  5, 8,  7, 10, 12, ... a permutation of the nonnegative integers A265734(n)
%C A272188 etc.
%C A272188 A005843(n) - A005843(n-1) = 2, for n>0.
%C A272188 A265667(n) - A265667(n-3) = 4, 2, 4 (period 3), for n>2.
%C A272188 A265734(n) - A265734(n-5) = 6, 4, 6, 4, 6 (period 5), for n>4.
%C A272188 See A267654.
%C A272188 For
%C A272188 1, 3, 5, 7, 9, 11, 13 ... the odd numbers A005408(n),
%C A272188 0, 1, 3, 2, 5,  7,  4, 9, 11, ... a permutation of the nonnegative numbers A006369,
%C A272188 0, 1, 2, 3, 5,  4,  7, 6,  9, 11, 8, 13, 10, 15, ... another permutation,
%C A272188 a(n) must be extended with one term by row:
%C A272188 1, 3,
%C A272188 0, 1, 3, 2,
%C A272188 0, 1, 2, 3, 5, 4,
%e A272188 Irregular triangle:
%e A272188 1,
%e A272188 0, 1, 3,
%e A272188 0, 1, 2, 3, 5,
%e A272188 0, 1, 2, 3, 4, 5, 7,
%e A272188 0, 1, 2, 3, 4, 5, 6, 7, 9,
%e A272188 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11,
%e A272188 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13,
%e A272188 etc.
%t A272188 Table[Delete[Range[0, 2 n + 1], 2 n + 1], {n, 0, 8}] // Flatten (* _Michael De Vlieger_, Apr 25 2016 *)
%Y A272188 Cf. A001477, A005408, A005843, A006369, A028310 (main diagonal), A053186, A265667, A265734, A267654.
%K A272188 nonn,tabf,easy
%O A272188 0,4
%A A272188 _Paul Curtz_, Apr 22 2016