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

Author

Clark Kimberling, May 14 2004

Keywords

• nonn
• tabl

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

Examples

			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;
		

Links

• Michel Marcus, Rows n=0..99 of triangle, flattened

Crossrefs

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

Cf. A048473, A171498, A198644

Programs

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

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

Extensions

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