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A094617 Triangular array T of numbers generated by these rules: 2 is in T; and if x is in T, then 2x-1 and 3x-2 are in T. 4
2, 3, 4, 5, 7, 10, 9, 13, 19, 28, 17, 25, 37, 55, 82, 33, 49, 73, 109, 163, 244, 65, 97, 145, 217, 325, 487, 730, 129, 193, 289, 433, 649, 973, 1459, 2188, 257, 385, 577, 865, 1297, 1945, 2917, 4375, 6562, 513, 769, 1153, 1729, 2593, 3889, 5833, 8749, 13123, 19684 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

To obtain row n from row n-1, apply 2x-1 to each x in row n-1 and then put 1+3^n at the end. Or, instead, apply 3x-2 to each x in row n-1 and then put 1+2^n at the beginning.

From Lamine Ngom, Feb 10 2021: (Start)

Triangle read by diagonals provides all the sequences of the form 1+2^(k-1)*3^n, where k is the k-th diagonal.

For instance, the terms of the first diagonal form the sequence 2, 4, 10, 28, ..., i.e., 1+3^n (A034472).

The 2nd diagonal leads to the sequence 3, 7, 19, 55, ..., i.e., 1+2*3^n (A052919).

The 3rd diagonal is the sequence 5, 13, 37, 109, ..., i.e., 1+4*3^n (A199108).

And for k = 4, we obtain the sequence 9, 25, 73, 217, ..., i.e., 1+8*3^n (A199111). (End)

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..5151

FORMULA

When offset is zero, then the first term is T(0,0) = 2, and

T(n,0) = 1 + 2^n = A000051(n),

T(n,n) = 1 + 3^n = A048473(n),

T(2n,n) = 1 + 6^n = A062394(n).

Row sums = A094618.

a(n) = A036561(n-1) + 1. - Filip Zaludek, Nov 19 2016

EXAMPLE

Rows of this triangle begin:

    2;

    3,   4;

    5,   7,   10;

    9,  13,   19,   28;

   17,  25,   37,   55,   82;

   33,  49,   73,  109,  163,  244;

   65,  97,  145,  217,  325,  487,  730;

  129, 193,  289,  433,  649,  973, 1459, 2188;

  257, 385,  577,  865, 1297, 1945, 2917, 4375,  6562;

  513, 769, 1153, 1729, 2593, 3889, 5833, 8749, 13123, 19684;

  ...

MATHEMATICA

FoldList[Append[2 #1 - 1, 1 + 3^#2] &, {2}, Range[9]] // Flatten (* Ivan Neretin, Mar 30 2016 *)

CROSSREFS

Cf. A094616, A094618, A138247.

Cf. A034472, A052919, A199108, A199111.

Sequence in context: A118463 A214652 A137929 * A254318 A047502 A117092

Adjacent sequences:  A094614 A094615 A094616 * A094618 A094619 A094620

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, May 14 2004

STATUS

approved

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Last modified October 23 19:26 EDT 2021. Contains 348215 sequences. (Running on oeis4.)