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 A160124 Total number of squares and rectangles after n stages in the toothpick structure of A139250. 20
 0, 0, 0, 2, 4, 4, 8, 18, 24, 24, 28, 36, 40, 44, 64, 94, 108, 108, 112, 120, 124, 128, 148, 176, 188, 192, 208, 228, 240, 268, 340, 418, 448, 448, 452, 460, 464, 468, 488, 516, 528, 532, 548, 568, 580, 608, 680, 756, 784, 788, 804, 824, 836, 864, 932, 1000, 1028 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS From Omar E. Pol, Sep 16 2012: (Start) It appears that A147614(n)/a(n) converge to 2. It appears that A139250(n)/a(n) converge to 3/2. It appears that a(n)/A139252(n) converge to 2. (End) Also 0 together with the rows sums of A211008. - Omar E. Pol, Sep 24 2012 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.] Brian Hayes, Joshua Trees and Toothpicks N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS FORMULA See A160125 for a recurrence. - N. J. A. Sloane, Feb 03 2010 a(n) = 1+2*A139250(n)-A147614(n), n>0 (Euler's formula). [From R. J. Mathar, Jan 22 2010] a(n) = A187220(n+1) - A147614(n), n>0. - Omar E. Pol, Feb 15 2013 MATHEMATICA w [n_] := w[n] = Module[{k, i}, Which[n == 0, 0, n <= 3, n - 1, True, k = Floor[Log[2, n]]; i = n - 2^k; Which[i == 0, 2^(k - 1) - 1, i < 2^k - 2, 2 w[i] + w[i + 1], i == 2^k - 2, 2 w[i] + w[i + 1] + 1, True, 2 w[i] + w[i + 1] + 2]]]; r[n_] := r[n] = Module[{k, i}, Which[n <= 2, 0, n <= 4, 2, True, k = Floor[Log[2, n]]; i = n - 2^k; Which[i == 0, 2^k - 2, i <= 2^k - 2, 4 w[i], True, 4 w[i] + 2]]]; Join[{0}, Array[r, 100]] // Accumulate (* Jean-François Alcover, Apr 15 2020, after Maple code in A160125 *) CROSSREFS Cf. A139250, A139252, A147614, A159786, A159787, A159788, A159789, A160125, A160126, A160127. Sequence in context: A089887 A161816 A240347 * A295293 A080007 A239649 Adjacent sequences:  A160121 A160122 A160123 * A160125 A160126 A160127 KEYWORD nonn AUTHOR Omar E. Pol, May 03 2009 EXTENSIONS More terms from R. J. Mathar, Jan 21 2010 STATUS approved

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Last modified October 30 16:01 EDT 2020. Contains 338081 sequences. (Running on oeis4.)