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 A152998 Toothpick sequence on the semi-infinite square grid. 14
 0, 1, 3, 5, 7, 11, 17, 21, 23, 27, 33, 39, 47, 61, 77, 85, 87, 91, 97, 103, 111, 125, 141, 151, 159, 173, 191, 211, 241, 285, 325, 341, 343, 347, 353, 359, 367, 381, 397, 407, 415, 429, 447, 467, 497, 541, 581, 599, 607, 621, 639 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Contribution from Omar E. Pol, Oct 01 2011 (Start): On the semi-infinite square grid, at stage 0, we start from a vertical half toothpick at [(0,0),(0,1)]. This half toothpick represents one of the two components of the first toothpick placed in the toothpick structure of A139250. Consider only the toothpicks of length 2, so a(0) = 0. At stage 1, we place an orthogonal toothpick of length 2 centered at the end, so a(1) = 1. In each subsequent stage, for every exposed toothpick end, place an orthogonal toothpick centered at that end. The sequence gives the number of toothpicks after n stages. A152968 (the first differences) gives the number of toothpicks added to the structure at n-th stage. For more information see A139250. (End) 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 FORMULA a(n) = (A139250(n+1)-1)/2. Contribution from Omar E. Pol, Oct 01 2011 (Start): a(n) = A139250(n+1) - A153003(n) + A153000(n-1) - 1, if n >= 1. a(n) = A153003(n) - A153000(n-1), if n >= 1. a(n) = 2*A153000(n-1) + 1, if n >= 1. (End) a(n) = (A187220(n+2) - 3)/4. - Omar E. Pol, Feb 18 2013 CROSSREFS Cf. A139250, A139251, A152968. Cf. A153000, A152978. Sequence in context: A094342 A045397 A211409 * A222176 A108539 A170886 Adjacent sequences:  A152995 A152996 A152997 * A152999 A153000 A153001 KEYWORD nonn AUTHOR Omar E. Pol, Dec 19 2008, Dec 23 2008, Jan 02 2008 STATUS approved

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Last modified February 19 06:46 EST 2018. Contains 299330 sequences. (Running on oeis4.)