A151930 First differences of A001316.

1, 0, 2, -2, 2, 0, 4, -6, 2, 0, 4, -4, 4, 0, 8, -14, 2, 0, 4, -4, 4, 0, 8, -12, 4, 0, 8, -8, 8, 0, 16, -30, 2, 0, 4, -4, 4, 0, 8, -12, 4, 0, 8, -8, 8, 0, 16, -28, 4, 0, 8, -8, 8, 0, 16, -24, 8, 0, 16, -16, 16, 0, 32, -62, 2, 0, 4, -4, 4, 0, 8, -12, 4, 0, 8, -8, 8, 0, 16, -28, 4, 0, 8, -8, 8, 0, 16, -24, 8, 0, 16, -16, 16, 0, 32

Offset

0,3

Comments

Net increase in number of ON cells at generation n of 1-D CA using Rule 90.

Links

Table of n, a(n) for n=0..94.

Index entries for sequences related to cellular automata

Formula

a((2*n+1)*2^p-1) = (2-2^p) * A001316(n), p >= 0 and n >=0. - Johannes W. Meijer, Jan 25 2013

G.f.: -1/x + ((1 - x)/x)*Product_{k>=0} (1 + 2*x^(2^k)). - Ilya Gutkovskiy, Feb 28 2017

Maple

nmax := 94: A001316 := n -> if n<=-1 then 0 else 2^add(i, i=convert(n, base, 2)) fi: for p from 0 to ceil(log[2](nmax))+1 do for n from 0 to nmax/(p+2)+1 do a((2*n+1)*2^p-1) := (2-2^p) * A001316(n) od: od: seq(a(n), n=0..nmax); # Johannes W. Meijer, Jan 25 2013

Crossrefs

Cf. A001316, A220466.

Sequence in context: A125938 A215461 A158851 * A356907 A084203 A073358

Adjacent sequences: A151927 A151928 A151929 * A151931 A151932 A151933

Keyword

sign

Author

N. J. A. Sloane, Aug 10 2009

Status

approved