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A115218 Triangle read by rows: zeroth row is 0; to get row n >= 1, append next 2^n numbers to end of previous row.

%I A115218 #14 Jan 20 2021 12:40:20
%S A115218 0,0,1,2,0,1,2,3,4,5,6,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,0,1,2,3,4,5,
%T A115218 6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
%U A115218 30,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22
%N A115218 Triangle read by rows: zeroth row is 0; to get row n >= 1, append next 2^n numbers to end of previous row.
%H A115218 Robert Israel, <a href="/A115218/b115218.txt">Table of n, a(n) for n = 0..10000</a>
%F A115218 From _Robert Israel_, Jan 02 2018: (Start)
%F A115218 G.f.: x^2/(1-x)^2 - (1-x)^(-1)*Sum_{n>=2} (2^n-1)*x^(2^(n+1)-n-2).
%F A115218 a(n) = k if n = 2^m - m + k - 1, 0 <= k <= 2^m-2.
%F A115218 G.f. as triangle: (1-y)^(-2)*Sum_{n>=1} x^n*(y + (1-2^n)*y^(2^n-1)+(2^n-2)*y^(2^n)). (End)
%e A115218 Triangle begins:
%e A115218 0
%e A115218 0 1 2
%e A115218 0 1 2 3 4 5 6
%e A115218 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
%e A115218 ...
%p A115218 seq($0..2^n-2, n=0..5); # _Robert Israel_, Jan 02 2018
%t A115218 Range[0,#-1]&/@Accumulate[2^Range[0,5]]//Flatten (* _Harvey P. Dale_, Jan 20 2021 *)
%Y A115218 Cf. A126646 (length of n-th row).
%K A115218 nonn,tabf
%O A115218 0,4
%A A115218 _N. J. A. Sloane_, based on a suggestion from _Harrie Grondijs_, Mar 04 2006