A094615 - OEIS

%I #37 Mar 23 2021 21:21:07

%S 1,3,5,7,11,17,15,23,35,53,31,47,71,107,161,63,95,143,215,323,485,127,

%T 191,287,431,647,971,1457,255,383,575,863,1295,1943,2915,4373,511,767,

%U 1151,1727,2591,3887,5831,8747,13121,1023,1535,2303,3455,5183,7775,11663,17495,26243,39365

%N 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 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 Subtriangle of the triangle in A230445. - _Philippe Deléham_, Oct 31 2013

%H Michel Marcus, <a href="/A094615/b094615.txt">Rows n=0..99 of triangle, flattened</a>

%F T(n,0) = -1+2^(n+1) = A000225(n+1).

%F T(n,n) = -1+2*3^n = A048473(n).

%F T(2n,n) = -1+2*6^n.

%F T(n,k) = -1 + 2^(n+1-k)*3^k. - _Lamine Ngom_, Feb 10 2021

%e Triangle begins:

%e   n\k|   1    2    3    4    5    6     7

%e   ---+-----------------------------------

%e   0  |   1;

%e   1  |   3,   5;

%e   2  |   7,  11,  17;

%e   3  |  15,  23,  35,  53;

%e   4  |  31,  47,  71, 107, 161;

%e   5  |  63,  95, 143, 215, 323, 485;

%e   6  | 127, 191, 287, 431, 647, 971, 1457;

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

%Y Cf. A048473, A171498, A198644

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, May 14 2004

%E Offset 0 and more terms from _Michel Marcus_, Nov 14 2020