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

0,4

Links

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

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)

Example

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
...

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 *)

Crossrefs

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

Sequence in context: A135317 A332663 A227179 * A023858 A011118 A354773

Adjacent sequences: A115215 A115216 A115217 * A115219 A115220 A115221

Keyword

nonn,tabf

Author

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

Status

approved