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

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, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22

Offset: 0

Author

N. J. A. Sloane, based on a suggestion from Harrie Grondijs, Mar 04 2006

Keywords

• nonn
• tabf

Examples

			Triangle begins:
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
...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

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

Programs

Maple

seq($0..2^n-2, n=0..5); # Robert Israel, Jan 02 2018

Mathematica

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

Formula

From Robert Israel, Jan 02 2018: (Start)

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

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

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)