A170842 G.f.: Product_{k>=1} (1 + 2x^(2^k-1) + 3x^(2^k)).

1, 2, 3, 2, 7, 12, 9, 2, 7, 12, 13, 20, 45, 54, 27, 2, 7, 12, 13, 20, 45, 54, 31, 20, 45, 62, 79, 150, 243, 216, 81, 2, 7, 12, 13, 20, 45, 54, 31, 20, 45, 62, 79, 150, 243, 216, 85, 20, 45, 62, 79, 150, 243, 224, 133, 150, 259, 344, 537, 936, 1161, 810, 243, 2, 7, 12, 13, 20, 45

Offset

0,2

Comments

From Omar E. Pol, Apr 10 2021: (Start)

It appears that this is also an irregular triangle read by rows (see the example).

It appears that right border gives A000244.

It appears that row sums give A052934. (End)

Links

John Tyler Rascoe, Table of n, a(n) for n = 0..8192

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Example

From Omar E. Pol, Apr 10 2021: (Start)
Written as an irregular triangle in which row lengths are A000079 the sequence begins:
1;
2, 3;
2, 7, 12, 9;
2, 7, 12, 13, 20, 45, 54, 27;
2, 7, 12, 13, 20, 45, 54, 31, 20, 45, 62, 79, 150, 243, 216, 81;
2, 7, 12, 13, 20, 45, 54, 31, 20, 45, 62, 79, 150, 243, 216, 85, 20, 45, 62, ...
(End)

Mathematica

CoefficientList[Series[Product[1+2x^(2^k-1)+3x^2^k, {k, 10}], {x, 0, 70}], x] (* Harvey P. Dale, Apr 09 2021 *)

Prog

(PARI)
D_x(N) = {my( x='x+O('x^N)); Vec(prod(k=1, logint(N, 2)+1, (1+2*x^(2^k-1)+3*x^(2^k))))}
D_x((2^6)+1) \\ John Tyler Rascoe, Aug 16 2024

Crossrefs

Cf. A000079, A000244, A052934, A275667.

Sequence in context: A209774 A271322 A373420 * A014784 A048601 A008317

Adjacent sequences: A170839 A170840 A170841 * A170843 A170844 A170845

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jan 02 2010

Status

approved