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
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
Programs
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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
Comments