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 A151781 #27 Oct 31 2022 12:12:10 %S A151781 1,7,13,43,49,79,109,259,265,295,325,475,505,655,805,1555,1561,1591, %T A151781 1621,1771,1801,1951,2101,2851,2881,3031,3181,3931,4081,4831,5581, %U A151781 9331,9337,9367,9397,9547,9577,9727,9877,10627,10657,10807,10957,11707,11857,12607 %N A151781 Partial sums of A151779. %C A151781 Total number of ON cells after n-th generation of cellular automaton based on Z^3 lattice in the same way that A147562 is based on the Z^2 lattice. Here each cell has six neighbors. %H A151781 Charles R Greathouse IV, <a href="/A151781/b151781.txt">Table of n, a(n) for n = 1..10000</a> %H A151781 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 A151781 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. 32-33. %H A151781 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 A151781 a[n_] := 6*5^(Total@ IntegerDigits[n - 1, 2] - 1); a[1] = 1; Accumulate@ Array[a, 46] (* _Michael De Vlieger_, Oct 31 2022 *) %o A151781 (PARI) a(n)=sum(k=1,n,6*5^(hammingweight(k-1)-1)\1) \\ _Charles R Greathouse IV_, Sep 14 2015 %Y A151781 Cf. A147562, A151779, A151790, A151792, A151793. %K A151781 nonn,look %O A151781 1,2 %A A151781 _N. J. A. Sloane_, Jun 25 2009