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
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jan 02 2010
STATUS
approved