The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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), 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 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015 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 a(n) = A147646(n) - a(n-1), 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^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 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] (* Jean-François 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 7 05:20 EDT 2020. Contains 334837 sequences. (Running on oeis4.)