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A151548
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When A160552 is regarded as a triangle with rows of lengths 1, 1, 2, 4, 8, 16, ..., this is what the rows converge to.
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7
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), May 25 2009: 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,...).
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 04 2009: (Start)
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). (End)
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LINKS
| David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
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FORMULA
| a(2^k-1) = 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^i-2. - N. J. A. Sloane, May 22 2009
G.f.: 1/(1+x) + 4*x*mul(1+x^(2^k-1)+2*x^(2^k),k=1..oo). - N. J. A. Sloane, May 23 2009
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EXAMPLE
| Contribution from Omar E. Pol (info(AT)polprimos.com), Jul 24 2009: (Start)
If 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)
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MAPLE
| G := 1/(1+x) + 4*x*mul(1+x^(2^k-1)+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:=n-2^i;
if j=0 then 5 elif j=2^i-1 then 2*n+1
else 2*S2(j)+S2(j+1); fi;
end; # - N. J. A. Sloane, May 22 2009
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CROSSREFS
| Cf. A139250, A160552, A151549.
A078008 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 25 2009]
Sequence in context: A141261 A077129 A073409 * A177433 A071581 A184722
Adjacent sequences: A151545 A151546 A151547 * A151549 A151550 A151551
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KEYWORD
| nonn
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AUTHOR
| David Applegate (david(AT)research.att.com), May 18 2009
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