

A151548


When A160552 is regarded as a triangle with rows of lengths 1, 1, 2, 4, 8, 16, ..., this is what the rows converge to.


16



1, 3, 5, 7, 5, 11, 17, 15, 5, 11, 17, 19, 21, 39, 49, 31, 5, 11, 17, 19, 21, 39, 49, 35, 21, 39, 53, 59, 81, 127, 129, 63, 5, 11, 17, 19, 21, 39, 49, 35, 21, 39, 53, 59, 81, 127, 129, 67, 21, 39, 53, 59, 81, 127, 133, 91, 81, 131, 165, 199, 289, 383, 321, 127, 5, 11, 17, 19, 21, 39
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OFFSET

0,2


COMMENTS

When convolved with A151575: (1, 0, 2, 2, 6, 10, 22, 42, 86, 170, 342, ...) equals the toothpick sequence A139250: (1, 3, 7, 11, 15, 23, 35, 43, ...).  Gary W. Adamson, May 25 2009
Equals A160552: [1, 1, 3, 1, 3, 5, ...] convolved with [1, 2, 0, 0, 0, ...], equivalent to a(n) = 2*A160552(n) + A160552(n+1).  Gary W. Adamson, Jun 04 2009
Equals (1, 0, 2, 2, 2, 2, ...) convolved with the Toothpick sequence, A139250.  Gary W. Adamson, Mar 06 2012
It appears that the sums of two successive terms give A147646.  Omar E. Pol, Feb 18 2015


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..10000
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015


FORMULA

a(2^k1) = 2^(k+1)1 for k >= 0; otherwise a(2^k) = 5 for k >= 1; otherwise a(2^i+j) = 2a(j)+a(j+1) for i >= 2, 1 <= j <= 2^i2.  N. J. A. Sloane, May 22 2009
G.f.: 1/(1+x) + 4*x*mul(1+x^(2^k1)+2*x^(2^k),k=1..oo).  N. J. A. Sloane, May 23 2009
a(n) = A147646(n)  a(n1), n >= 1.  Omar E. Pol, Feb 19 2015


EXAMPLE

From Omar E. Pol, Jul 24 2009: (Start)
When written as a triangle:
1;
3;
5,7;
5,11,17,15;
5,11,17,19,21,39,49,31;
5,11,17,19,21,39,49,35,21,39,53,59,81,127,129,63;
5,11,17,19,21,39,49,35,21,39,53,59,81,127,129,67,21,39,53,59,81,127,133,91,...
(End)


MAPLE

G := 1/(1+x) + 4*x*mul(1+x^(2^k1)+2*x^(2^k), k=1..20); # N. J. A. Sloane, May 23 2009
S2:=proc(n) option remember; local i, j;
if n <= 1 then RETURN(2*n+1); fi;
i:=floor(log(n)/log(2));
j:=n2^i;
if j=0 then 5 elif j=2^i1 then 2*n+1
else 2*S2(j)+S2(j+1); fi;
end; #  N. J. A. Sloane, May 22 2009


MATHEMATICA

terms = 70; CoefficientList[1/(1 + x) + 4*x*Product[1 + x^(2^k  1) + 2*x^(2^k), {k, 1, Log[2, terms] // Ceiling}] + O[x]^terms, x] (* JeanFrançois Alcover, Nov 14 2017, after N. J. A. Sloane *)


CROSSREFS

Cf. A139250, A160552, A151549, A078008, A246336, A147646, A151575.
Sequence in context: A077129 A073409 A260234 * A256258 A177433 A264827
Adjacent sequences: A151545 A151546 A151547 * A151549 A151550 A151551


KEYWORD

nonn


AUTHOR

David Applegate, May 18 2009


STATUS

approved



