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First differences of A001316.
2

%I #12 Feb 28 2017 07:45:40

%S 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,

%T 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,

%U 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

%N First differences of A001316.

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

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%F a((2*n+1)*2^p-1) = (2-2^p) * A001316(n), p >= 0 and n >=0. - _Johannes W. Meijer_, Jan 25 2013

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

%p 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

%Y Cf. A001316, A220466.

%K sign

%O 0,3

%A _N. J. A. Sloane_, Aug 10 2009