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 A151688 G.f.: Prod_{ n >= 0} (1 + x^(2^n-1) + 2*x^(2^n)). 14
 2, 4, 6, 6, 8, 14, 16, 10, 8, 14, 18, 20, 30, 44, 40, 18, 8, 14, 18, 20, 30, 44, 42, 28, 30, 46, 56, 70, 104, 128, 96, 34, 8, 14, 18, 20, 30, 44, 42, 28, 30, 46, 56, 70, 104, 128, 98, 44, 30, 46, 56, 70, 104, 130, 112, 86, 106, 148, 182, 244, 336, 352, 224, 66, 8, 14, 18, 20, 30, 44 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This is essentially the same g.f. as A151550 but with the n=0 term included. LINKS 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 FORMULA a(n) = Sum_{k >= 0} 2^(wt(n+k)-k)*binomial(wt(n+k),k). EXAMPLE If written as a triangle, begins: .2; .4; .6,6; .8,14,16,10, .8,14,18,20,30,44,40,18, .8,14,18,20,30,44,42,28,30,46,56,70,104,128,96,34, .... CROSSREFS Equals 2*A152980 = A147646/2. Equals limit of rows of triangle in A152968. For generating functions of the form Prod_{k>=c} (1+a*x^(2^k-1)+b*x^2^k)) for the following values of (a,b,c) see: (1,1,0) A160573, (1,1,1) A151552, (1,1,2) A151692, (2,1,0) A151685, (2,1,1) A151691, (1,2,0) A151688 and A152980, (1,2,1) A151550, (2,2,0) A151693, (2,2,1) A151694 Cf. A151550, A139251, A139250. Sequence in context: A023853 A056526 A049066 * A159276 A056942 A115947 Adjacent sequences:  A151685 A151686 A151687 * A151689 A151690 A151691 KEYWORD nonn,tabf AUTHOR Omar E. Pol, May 02 2009 EXTENSIONS Edited by N. J. A. Sloane, Jun 03 2009, Jul 14 2009 STATUS approved

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Last modified September 20 05:58 EDT 2020. Contains 337264 sequences. (Running on oeis4.)