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 A159912 #21 May 21 2023 14:49:16
%S A159912 0,1,4,7,14,17,24,31,46,49,56,63,78,85,100,115,146,149,156,163,178,
%T A159912 185,200,215,246,253,268,283,314,329,360,391,454,457,464,471,486,493,
%U A159912 508,523,554,561,576,591,622,637,668,699,762,769,784,799,830,845,876,907
%N A159912 Partial sums of A159913(k) = 2^bitcount(2k+1)-1 = A038573(2k+1), bitcount=A000120.
%C A159912 More precisely, a(n)=sum(i<n, A159913(i)), since we want the sequence to start with a(0)=0 and not with A159913(0)=1.
%C A159912 a(n) is also the total number of ON cells after n generations in the outward corner version of the Ulam-Warburton cellular automaton of A147562, and a(n) is also the total number of Y-toothpicks after n generations in the outward corner version of the Y-toothpick structure of A160120. - _David Applegate_ and _Omar E. Pol_, Jan 24 2016
%H A159912 Paolo Xausa, <a href="/A159912/b159912.txt">Table of n, a(n) for n = 0..10000</a>
%H A159912 David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a>
%H A159912 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, pp. 6, 30.
%H A159912 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 A159912 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A159912 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%F A159912 a(n) = sum( i=0...n-1, A159913(i)) = sum(i=0..n-1, 2^A000120(i))*2-n
%F A159912 a(n) = n + (A160720(n) - 1)/2 = n + 2*(A266532(n) - 1)/3 = n + 2*A267700(n-1), n >= 1. - _Omar E. Pol_, Jan 25 2016
%t A159912 Accumulate@ Table[2^(DigitCount[n, 2][[1]] + 1) - 1, {n, 0, 54}] (* _Michael De Vlieger_, Jan 25 2016 *)
%o A159912 (PARI) A159912(n)=sum(i=0,n-1,1<<norml2(binary(i)))*2-n
%Y A159912 Cf. A000120, A038573, A147562, A159913, A160120, A160720, A266532, A267700.
%K A159912 nonn
%O A159912 0,3
%A A159912 _M. F. Hasler_, May 03 2009