A064766 Fill up an infinite triangular array by rows by successively writing numbers 1, then 1 up to 2*3/2, then 1 up to 3*4/2, then 1 up to 4*5/2 and so on, at the k-th step writing the numbers from 1 up to the k-th triangular number. The final elements of the rows of this infinite triangle form the sequence.

1, 2, 2, 6, 5, 1, 8, 1, 10, 20, 10, 22, 7, 21, 36, 16, 33, 6, 25, 45, 11, 33, 56, 14, 39, 65, 14, 42, 71, 10, 41, 73, 1, 35, 70, 106, 23, 61, 100, 4, 45, 87, 130, 21, 66, 112, 159, 36, 85, 135, 186, 48, 101, 155, 210, 56, 113, 171, 230, 59, 120, 182, 245, 56, 121, 187

Offset: 0

Author

Floor van Lamoen, Oct 18 2001

Keywords

• easy
• nonn

Comments

An alternative, equivalent, definition: Let T(i) = [1,2,3,...,i*(i+1)/2], and let S be the concatenation of T(1), T(2), ... Create a triangle by partitioning S into rows of lengths 1, 2, 3, ... The right-hand elements of the rows of this triangle form the new sequence.

Examples

			The first few stages in the construction of the triangular array are:
1
then
..1
.1.2.
3
then
...1
..1.2
.3.1.2
3.4.5.6
then
.....1
....1.2
...3.1.2
..3.4.5.6
.1.2.3.4.5
6.7.8.9.10.
The right-most diagonal forms the sequence: 1,2,2,6,5,...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Mini-index to these sequences: A064766, A064865, A064866, A065221-A655234 are all of the same type. See A064766 for a detailed explanation.

Programs

Mathematica

With[{nn=75},TakeList[Flatten[Range[1,#]&/@Accumulate[Range[nn]]],Range[nn]][[;;,-1]]] (* Harvey P. Dale, Oct 31 2024 *)

Extensions

Edtied by N. J. A. Sloane, Oct 31 2024