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.

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

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

Cf. A094616 (row sums), A094617, A230445.

Cf. A048473, A171498, A198644

Sequence in context: A019449 A373554 A219533 * A245396 A144574 A082373

Adjacent sequences: A094612 A094613 A094614 * A094616 A094617 A094618

Keyword

nonn,tabl

Author

Clark Kimberling, May 14 2004

Extensions

Offset 0 and more terms from Michel Marcus, Nov 14 2020

Status

approved