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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.

%I A094615 #37 Mar 23 2021 21:21:07
%S A094615 1,3,5,7,11,17,15,23,35,53,31,47,71,107,161,63,95,143,215,323,485,127,
%T A094615 191,287,431,647,971,1457,255,383,575,863,1295,1943,2915,4373,511,767,
%U A094615 1151,1727,2591,3887,5831,8747,13121,1023,1535,2303,3455,5183,7775,11663,17495,26243,39365
%N 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.
%C A094615 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.
%C A094615 Subtriangle of the triangle in A230445. - _Philippe Deléham_, Oct 31 2013
%H A094615 Michel Marcus, <a href="/A094615/b094615.txt">Rows n=0..99 of triangle, flattened</a>
%F A094615 T(n,0) = -1+2^(n+1) = A000225(n+1).
%F A094615 T(n,n) = -1+2*3^n = A048473(n).
%F A094615 T(2n,n) = -1+2*6^n.
%F A094615 T(n,k) = -1 + 2^(n+1-k)*3^k. - _Lamine Ngom_, Feb 10 2021
%e A094615 Triangle begins:
%e A094615   n\k|   1    2    3    4    5    6     7
%e A094615   ---+-----------------------------------
%e A094615   0  |   1;
%e A094615   1  |   3,   5;
%e A094615   2  |   7,  11,  17;
%e A094615   3  |  15,  23,  35,  53;
%e A094615   4  |  31,  47,  71, 107, 161;
%e A094615   5  |  63,  95, 143, 215, 323, 485;
%e A094615   6  | 127, 191, 287, 431, 647, 971, 1457;
%o A094615 (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
%Y A094615 Cf. A094616 (row sums), A094617, A230445.
%Y A094615 Cf. A048473, A171498, A198644
%K A094615 nonn,tabl
%O A094615 0,2
%A A094615 _Clark Kimberling_, May 14 2004
%E A094615 Offset 0 and more terms from _Michel Marcus_, Nov 14 2020