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 A152980 First differences of toothpick corner sequence A153006. 50
 1, 2, 3, 3, 4, 7, 8, 5, 4, 7, 9, 10, 15, 22, 20, 9, 4, 7, 9, 10, 15, 22, 21, 14, 15, 23, 28, 35, 52, 64, 48, 17, 4, 7, 9, 10, 15, 22, 21, 14, 15, 23, 28, 35, 52, 64, 49, 22, 15, 23, 28, 35, 52, 65, 56, 43, 53, 74, 91, 122, 168, 176, 112, 33, 4, 7, 9, 10, 15, 22, 21, 14, 15, 23, 28, 35, 52 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Rows of A152978 when written as a triangle converge to this sequence. - Omar E. Pol, Jul 19 2009 LINKS N. J. A. Sloane, Table of n, a(n) for n = 0..16384 David Applegate, The movie version 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 G.f.: (1 + x) * Prod_{ n >= 1} (1 + x^(2^n-1) + 2*x^(2^n)). - N. J. A. Sloane, May 20 2009, corrected May 21 2009 For formula see A147646 (or, better, see the Maple code below). EXAMPLE Triangle begins: .1; .2; .3,3; .4,7,8,5; .4,7,9,10,15,22,20,9; .4,7,9,10,15,22,21,14,15,23,28,35,52,64,48,17; .... Rows converge to A153001. - N. J. A. Sloane, Jun 07 2009 MAPLE Maple code from N. J. A. Sloane, May 18 2009. First define old version with offset 1: S:=proc(n) option remember; local i, j; if n <= 0 then RETURN(0); fi; if n <= 2 then RETURN(2^(n-1)); fi; i:=floor(log(n)/log(2)); j:=n-2^i; if j=0 then RETURN(n/2+1); fi; if j<2^i-1 then RETURN(2*S(j)+S(j+1)); fi; if j=2^i-1 then RETURN(2*S(j)+S(j+1)-1); fi; -1; end; # Now change the offset: T:=n->S(n+1); G := (1 + x) * mul(1 + x^(2^k-1) + 2*x^(2^k), k=1..20); CROSSREFS Equals A151688 divided by 2. - N. J. A. Sloane, Jun 03 2009 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. Equals A147646/4. - N. J. A. Sloane, May 01 2009 Cf. A139250, A139251, A152968, A152978, A153006, A153001, A159785, A153004. Sequence in context: A260167 A035540 A114863 * A170891 A035535 A154309 Adjacent sequences:  A152977 A152978 A152979 * A152981 A152982 A152983 KEYWORD nonn,look AUTHOR Omar E. Pol, Dec 16 2008, Dec 19 2008, Jan 02 2009 EXTENSIONS More terms (based on A147646) from N. J. A. Sloane, May 01 2009 Offset changed by N. J. A. Sloane, May 18 2009 STATUS approved

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Last modified September 28 04:53 EDT 2021. Contains 347703 sequences. (Running on oeis4.)