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A094615
Triangular array T of numbers generated by these rules: 1 is in T; and if x is in T, then 2x+1 and 3x+2 are in T.
3
1, 3, 5, 7, 11, 17, 15, 23, 35, 53, 31, 47, 71, 107, 161, 63, 95, 143, 215, 323, 485, 127, 191, 287, 431, 647, 971, 1457, 255, 383, 575, 863, 1295, 1943, 2915, 4373, 511, 767, 1151, 1727, 2591, 3887, 5831, 8747, 13121, 1023, 1535, 2303, 3455, 5183, 7775, 11663, 17495, 26243, 39365
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
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
Cf. A094616 (row sums), A094617, A230445.
Sequence in context: A019449 A373554 A219533 * A245396 A144574 A082373
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, May 14 2004
EXTENSIONS
Offset 0 and more terms from Michel Marcus, Nov 14 2020
STATUS
approved