OFFSET
1,1
COMMENTS
To obtain row n from row n-1, apply 2x-1 to each x in row n-1 and then put 1+3^n at the end. Or, instead, apply 3x-2 to each x in row n-1 and then put 1+2^n at the beginning.
From Lamine Ngom, Feb 10 2021: (Start)
Triangle read by diagonals provides all the sequences of the form 1+2^(k-1)*3^n, where k is the k-th diagonal.
For instance, the terms of the first diagonal form the sequence 2, 4, 10, 28, ..., i.e., 1+3^n (A034472).
The 2nd diagonal leads to the sequence 3, 7, 19, 55, ..., i.e., 1+2*3^n (A052919).
The 3rd diagonal is the sequence 5, 13, 37, 109, ..., i.e., 1+4*3^n (A199108).
And for k = 4, we obtain the sequence 9, 25, 73, 217, ..., i.e., 1+8*3^n (A199111). (End)
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..5151
FORMULA
EXAMPLE
Rows of this triangle begin:
2;
3, 4;
5, 7, 10;
9, 13, 19, 28;
17, 25, 37, 55, 82;
33, 49, 73, 109, 163, 244;
65, 97, 145, 217, 325, 487, 730;
129, 193, 289, 433, 649, 973, 1459, 2188;
257, 385, 577, 865, 1297, 1945, 2917, 4375, 6562;
513, 769, 1153, 1729, 2593, 3889, 5833, 8749, 13123, 19684;
...
MATHEMATICA
FoldList[Append[2 #1 - 1, 1 + 3^#2] &, {2}, Range[9]] // Flatten (* Ivan Neretin, Mar 30 2016 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, May 14 2004
STATUS
approved