

A162956


a(0) = 0, a(1) = 1; a(2^i + j) = 3a(j) + a(j + 1) for 0 <= j < 2^i.


6



0, 1, 1, 4, 1, 4, 7, 13, 1, 4, 7, 13, 7, 19, 34, 40, 1, 4, 7, 13, 7, 19, 34, 40, 7, 19, 34, 46, 40, 91, 142, 121, 1, 4, 7, 13, 7, 19, 34, 40, 7, 19, 34, 46, 40, 91, 142, 121, 7, 19, 34, 46, 40, 91, 142, 127, 40, 91, 148, 178, 211, 415, 547, 364, 1, 4, 7, 13, 7, 19, 34, 40, 7, 19, 34, 46
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OFFSET

0,4


COMMENTS

2^n term triangle by rows, analogous to A160552 but multiplier is "3" instead of "2"
Row sums = powers of 5: (1, 5, 25, 125, 625,...).
Rows tend to A162957, obtained by taking (1, 3, 0, 0, 0,...) * A162956.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..16383
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS


FORMULA

Follows the same analogous procedure as A160552 but multiplier is 3 instead of 2. (n+1)th row brings down nth row and appends to the right and equal number of terms following the rules: from left to right,let a = last term, b = current term, c = next term. Then c = 3*a + b except for the rightmost term = 3*a + 1.


EXAMPLE

The triangle begins:
0;
1;
1, 4;
1, 4, 7, 13;
1, 4, 7, 13, 7, 19, 34, 40;
1, 4, 7, 13, 7, 19, 34, 40, 7, 19, 34, 46, 40, 91, 142, 121;
...
Row 4 = (1, 4, 7, 13, 7, 19, 34, 40): brings down (1, 4, 7, 13) then 7 = 3*1 + 4, 19 = 3*4 + 7, 34 = 3*7 + 13, 40 = 3*13 + 1.


MAPLE

a:= proc(n) option remember; `if`(n<2, n,
(j> 3*a(j)+a(j+1))(n2^ilog2(n)))
end:
seq(a(n), n=0..100); # Alois P. Heinz, Jan 28 2017


MATHEMATICA

row[0] = {0}; row[1] = {1}; row[n_] := row[n] = Join[row[n1], 3 row[n1] + Append[Rest[row[n1]], 1]]; Table[row[n], {n, 0, 7}] // Flatten (* JeanFrançois Alcover, Mar 13 2017 *)


CROSSREFS

Cf. A162957, A162958, A160552.
Cf. A170838A170852, A170854A170872.
Sequence in context: A051006 A072812 A244097 * A131112 A141225 A079185
Adjacent sequences: A162953 A162954 A162955 * A162957 A162958 A162959


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Jul 18 2009


EXTENSIONS

Edited with more terms by N. J. A. Sloane, Jan 02 2010


STATUS

approved



