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 A151917 #27 Nov 02 2022 07:44:43
%S A151917 0,1,3,5,11,13,19,25,43,45,51,57,75,81,99,117,171,173,179,185,203,209,
%T A151917 227,245,299,305,323,341,395,413,467,521,683,685,691,697,715,721,739,
%U A151917 757,811,817,835,853,907,925,979,1033,1195,1201,1219
%N A151917 a(0)=0, a(1)=1; for n>=2, a(n) = (2/3)*(Sum_{i=1..n-1} 3^wt(i)) + 1, where wt() = A000120().
%C A151917 Also, total number of "ON" cells at n-th stage in two of the four wedges of the "Ulam-Warburton" two-dimensional cellular automaton of A147562, but including the central ON cell. It appears that this is very close to A139250, the toothpick sequence. - _Omar E. Pol_, Feb 22 2015
%H A151917 Michel Marcus, <a href="/A151917/b151917.txt">Table of n, a(n) for n = 0..10000</a>
%H A151917 Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2210.10968">Identities and periodic oscillations of divide-and-conquer recurrences splitting at half</a>, arXiv:2210.10968 [cs.DS], 2022, p. 31.
%H A151917 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>
%H A151917 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A151917 a(n) = A151914(n)/4.
%F A151917 a(n) = A079315(2n)/4.
%F A151917 For n>=2, a(n) = 2*A151920(n-2) + 1.
%F A151917 For n>=1, a(n) = (1 + A147562(n))/2. - _Omar E. Pol_, Mar 13 2011
%F A151917 a(2^k) = A007583(k), if k >= 0. - _Omar E. Pol_, Feb 22 2015
%e A151917 n=3: (2/3)*(3^1+3^1+3^2+3^1) + 1 = (2/3)*18 + 1 = 13.
%t A151917 Array[(2/3) Sum[3^(Total@ IntegerDigits[i, 2]), {i, # - 1}] + 1 &, 50] (* _Michael De Vlieger_, Nov 01 2022 *)
%o A151917 (PARI) a(n) = if (n<2, n, 1 + 2*sum(i=1,n-1, 3^hammingweight(i))/3); \\ _Michel Marcus_, Feb 22 2015
%Y A151917 Cf. A000120, A007583, A139250, A147562, A151914, A151920.
%K A151917 nonn,easy
%O A151917 0,3
%A A151917 _N. J. A. Sloane_, Aug 05 2009, Aug 06 2009