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 A147646 If A139251 is written as a triangle with rows of lengths 1, 2, 4, 8, 16, ..., the n-th row begins with 2^n followed by the first 2^n-1 terms of the present sequence. 13
 4, 8, 12, 12, 16, 28, 32, 20, 16, 28, 36, 40, 60, 88, 80, 36, 16, 28, 36, 40, 60, 88, 84, 56, 60, 92, 112, 140, 208, 256, 192, 68, 16, 28, 36, 40, 60, 88, 84, 56, 60, 92, 112, 140, 208, 256, 196, 88, 60, 92, 112, 140, 208, 260, 224, 172, 212, 296, 364, 488, 672, 704, 448, 132 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Limiting behavior of the rows of the triangle in A139251 when the first column of that triangle is omitted. First differences of A159795. - Omar E. Pol, Jul 24 2009 It appears that a(n) is also the number of new grid points that are covered at n-th stage of A139250 version "Tree", assuming the toothpicks have length 4, 3, and 2 (see also A159795 and A153006). - Omar E. Pol, Oct 25 2011 LINKS David Applegate, Table of n, a(n) for n = 1..2047 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 Letting n = 2^i + j for 0 <= j < 2^i, we have the recurrence (see A139251 for proof): a(1) = 4 a(2) = 8 a(n) = 2n+4 = 2*a(n/2) - 4 if j = 0 a(n) = 2*a(j) + a(j+1) - 4 if j = 2^i-1 a(n) = 2*a(j) + a(j+1) if 1 <= j < 2^i-1 It appears that a(n) = A151548(n-1) + A151548(n). - Omar E. Pol, Feb 19 2015 EXAMPLE Further comments: A139251 as a triangle is: . 1 . 2 4 . 4 4 8 12 . 8 4 8 12 12 16 28 32 . 16 4 8 12 12 16 28 32 20 16 28 36 40 60 88 80 . 32 4 8 12 12 16 28 32 20 16 28 36 40 60 88 80 36 16 28 36 40 60 88 84 56 ... leading to the present sequence: . 4 8 12 12 16 28 32 20 16 28 36 40 60 88 80 36 16 28 36 40 60 88 84 56 ... Note that this can also be written as a triangle: . 4 8 . 12 12 16 28 . 32 20 16 28 36 40 60 88 . 80 36 16 28 36 40 60 88 84 56 60 92 112 140 208 256 . 192 68 16 28 36 40 60 88 84 56 60 92 112 140 208 256 196 88 60 92 112 140 ... The first column is (n+1)2^n (where n is the row number), the second column is 2^(n+1)+4, and the rest exhibits the same constant column behavior, where the rows converge to: . 16 28 36 40 60 88 84 56 60 92 112 140 208 256 196 88 60 92 112 140 ... Once again this can be written as a triangle: . 16 . 28 36 40 60 . 88 84 56 60 92 112 140 208 . 256 196 88 60 92 112 140 208 260 224 172 212 296 364 488 672 . 704 452 152 60 92 112 140 208 260 224 172 212 296 364 488 672 708 480 236 ... and this behavior continues ad infinitum. MAPLE 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(2*n+4); 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)-4); fi; -1; end; # N. J. A. Sloane, May 18 2009 CROSSREFS Equals 2*A151688 and 4*A152980. - N. J. A. Sloane, Jul 16 2009 Cf. A139250, A139251, A153006, A159795, A151548. Sequence in context: A120427 A060830 A080458 * A080229 A284510 A167523 Adjacent sequences:  A147643 A147644 A147645 * A147647 A147648 A147649 KEYWORD nonn AUTHOR David Applegate, Apr 30 2009 STATUS approved

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Last modified August 23 11:24 EDT 2019. Contains 326222 sequences. (Running on oeis4.)