A115218 - OEIS

%I #14 Jan 20 2021 12:40:20

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

%H Robert Israel, <a href="/A115218/b115218.txt">Table of n, a(n) for n = 0..10000</a>

%F From _Robert Israel_, Jan 02 2018: (Start)

%F G.f.: x^2/(1-x)^2 - (1-x)^(-1)*Sum_{n>=2} (2^n-1)*x^(2^(n+1)-n-2).

%F a(n) = k if n = 2^m - m + k - 1, 0 <= k <= 2^m-2.

%F 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 Triangle begins:

%e 0

%e 0 1 2

%e 0 1 2 3 4 5 6

%e 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

%e ...

%p seq($0..2^n-2, n=0..5); # _Robert Israel_, Jan 02 2018

%t Range[0,#-1]&/@Accumulate[2^Range[0,5]]//Flatten (* _Harvey P. Dale_, Jan 20 2021 *)

%Y Cf. A126646 (length of n-th row).

%K nonn,tabf

%O 0,4

%A _N. J. A. Sloane_, based on a suggestion from _Harrie Grondijs_, Mar 04 2006