This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A163267 #16 Feb 24 2021 02:48:18
%S A163267 0,1,2,4,5,7,10,13,14,16,19,22,25,30,36,40,41,43,46,49,52,57,63,67,70,
%T A163267 75,81,87,95,106,116,121,122,124,127,130,133,138,144,148,151,156,162,
%U A163267 168,176,187,197,202,205,210,216,222,230,241,251,258,266,277,289,303,322,343,358
%N A163267 Partial sums of A118977.
%C A163267 Can be considered toothpick sequence for N=1.
%C A163267 Based on a consistent set of rules for generating toothpick sequences.
%C A163267 Cf. A139250 where (1, 1, 3, 1, 3, 5, 7, ...) is convolved with (1, 2, 2, 2, ...) and A162958 where A162956 is convolved with (1, 3, 3, 3, ...); the present sequence can be considered toothpick N=1 since A118977 is convolved with (1, 1, 1, ...).
%C A163267 Arranged in array fashion, the first three toothpick sequences would be:
%C A163267 N=1: A163267: (1, 2, 4, 5, 7, 10, 13, 14, ...)
%C A163267 N=2: A139250: (1, 3, 7, 11, 15, 23, 35, 43, ...)
%C A163267 N=3: A162958: (1, 4, 10, 19, 25, 40, 67, 94, ...)
%C A163267 ...
%C A163267 Is there an illustration of this sequence using toothpicks? - _Omar E. Pol_, Dec 13 2016
%H A163267 G. C. Greubel, <a href="/A163267/b163267.txt">Table of n, a(n) for n = 0..1000</a>
%H A163267 David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]
%H A163267 N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%t A163267 a[0] = 0; a[1] = 1; a[n_] := a[n] = (j = n - 2^Floor[Log[2, n]]; a[j] + a[j + 1]); Table[Sum[a[n], {n, 0, k}], {k, 0, 20}] (* _G. C. Greubel_, Dec 12 2016 *)
%Y A163267 Cf. A118977, A139250, A162958.
%K A163267 nonn
%O A163267 0,3
%A A163267 _Gary W. Adamson_, Jul 24 2009
%E A163267 Edited and extended by _N. J. A. Sloane_, Jan 07 2010