OFFSET
0,2
COMMENTS
To obtain row n from row n-1, apply 2x+1 to each x in row n-1 and then put -1+2*3^n at the end. Or, instead, apply 3x+2 to each x in row n-1 and then put -1+2^(n+1) at the beginning.
Subtriangle of the triangle in A230445. - Philippe Deléham, Oct 31 2013
LINKS
Michel Marcus, Rows n=0..99 of triangle, flattened
FORMULA
T(n,0) = -1+2^(n+1) = A000225(n+1).
T(n,n) = -1+2*3^n = A048473(n).
T(2n,n) = -1+2*6^n.
T(n,k) = -1 + 2^(n+1-k)*3^k. - Lamine Ngom, Feb 10 2021
EXAMPLE
Triangle begins:
n\k| 1 2 3 4 5 6 7
---+-----------------------------------
0 | 1;
1 | 3, 5;
2 | 7, 11, 17;
3 | 15, 23, 35, 53;
4 | 31, 47, 71, 107, 161;
5 | 63, 95, 143, 215, 323, 485;
6 | 127, 191, 287, 431, 647, 971, 1457;
PROG
(PARI) tabl(nn) = {my(row = [1], nrow); for (n=1, nn, print (row); nrow = vector(n+1, k, if (k<=n, (2*row[k]+1), -1+2*3^n)); row = nrow; ); } \\ Michel Marcus, Nov 14 2020
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, May 14 2004
EXTENSIONS
Offset 0 and more terms from Michel Marcus, Nov 14 2020
STATUS
approved