A256255 Triangle read by rows: T(n,k) = 6*k + 1, n>=0, 0<=k<=(2^n-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 *)

Crossrefs

Cf. A000225, A001235, A016921, A048488, A060867, A165665, A241717, A256258.

Sequence in context: A093564 A081776 A354128 * A131115 A151778 A138616

Adjacent sequences: A256252 A256253 A256254 * A256256 A256257 A256258

Keyword

nonn,tabf

Author

Omar E. Pol, Apr 30 2015

Status

approved