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

Author

N. J. A. Sloane, Jan 02 2010

Keywords

• nonn
• tabf

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)

Examples

			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)
		

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

Crossrefs

Cf. A000079, A000244, A052934, A275667.

Programs

Mathematica

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

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