login
A256255
Triangle read by rows: T(n,k) = 6*k + 1, n>=0, 0<=k<=(2^n-1).
1
1, 1, 7, 1, 7, 13, 19, 1, 7, 13, 19, 25, 31, 37, 43, 1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 181, 187, 1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103
OFFSET
0,3
COMMENTS
Row n lists the first 2^n terms of A016921, n >= 0.
Row sums give A165665.
Right border gives A048488.
The sum of all terms of the first k rows gives A060867(k).
The product of the terms of the third row is equal to the Hardy-Ramanujan number: 1 * 7 * 13 * 19 = 1729.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..16382 (rows 0..13 of the triangle, flattened)
EXAMPLE
Triangle begins:
1;
1,7;
1,7,13,19;
1,7,13,19,25,31,37,43;
1,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91;
...
Illustration of initial terms in the fourth quadrant of the square grid:
------------------------------------------------------------------------
n a(n) Compact diagram
------------------------------------------------------------------------
. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
0 1 |_|_ |_ _ _ |_ _ _ _ _ _ _ |
1 1 | |_| |_ _ | |_ _ _ _ _ _ | |
2 7 |_ _ _|_ | | |_ _ _ _ _ | | |
3 1 | | | |_| | | |_ _ _ _ | | | |
4 7 | | |_ _ _| | |_ _ _ | | | | |
5 13 | |_ _ _ _ _| |_ _ | | | | | |
6 19 |_ _ _ _ _ _ _|_ | | | | | | |
7 1 | | | | | | | |_| | | | | | | |
8 7 | | | | | | |_ _ _| | | | | | |
9 13 | | | | | |_ _ _ _ _| | | | | |
10 19 | | | | |_ _ _ _ _ _ _| | | | |
11 25 | | | |_ _ _ _ _ _ _ _ _| | | |
12 31 | | |_ _ _ _ _ _ _ _ _ _ _| | |
13 37 | |_ _ _ _ _ _ _ _ _ _ _ _ _| |
14 43 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
.
a(n) is also the number of cells in the n-th region of the diagram.
For other diagrams of the same family see A241717 and A256258.
MATHEMATICA
With[{rows=7}, Array[Range[1, 6*2^#, 6]&, rows, 0]] (* Paolo Xausa, Sep 26 2023 *)
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Apr 30 2015
STATUS
approved