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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.
17
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
0,2
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.
LINKS
EXAMPLE
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,...
MATHEMATICA
With[{nn=75}, TakeList[Flatten[Range[1, #]&/@Accumulate[Range[nn]]], Range[nn]][[;; , -1]]] (* Harvey P. Dale, Oct 31 2024 *)
CROSSREFS
Mini-index to these sequences: A064766, A064865, A064866, A065221-A655234 are all of the same type. See A064766 for a detailed explanation.
Sequence in context: A054516 A062400 A375851 * A019749 A209773 A209767
KEYWORD
easy,nonn,changed
AUTHOR
Floor van Lamoen, Oct 18 2001
EXTENSIONS
Edtied by N. J. A. Sloane, Oct 31 2024
STATUS
approved