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 A160704 #6 Feb 24 2021 02:48:18 %S A160704 1,3,9,19,41,87,181,363,729,1463,2933,5871,11753,23523,47061,94123, %T A160704 188249,376503,753013,1506031,3012073 %N A160704 Jacobsthal sequence A001045 convolved with A139251 (first differences of toothpick numbers). %H A160704 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 A160704 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> %F A160704 a(n) = 2*a(n-1) + A160552, where A160552 begins with offset 1: (1, 1, 3, 1, 3, 5, 7, 1, 3, 5, 7, 5,...). %e A160704 a(4) = 19 = (1, 1, 3, 5) dot (4, 4, 2, 1) = (4 + 4 + 6 + 5). %e A160704 a(4) = 19 = 2*9 + 1, where "1" = A160552(4), A160552 = (1, 1, 3, 1, 3, 5, 7,...) %e A160704 Using the latter method, we create a heading = row 1: %e A160704 1,...1,...3,...1,....3,...5,....7,....1,....3,.....5, = A160552 with offset 1. %e A160704 1...3,....9,...19,..41,..87,..181,..363,..729,..1463,... %e A160704 ...such that a(n) = 2*a(n-1) = term above a(n), or a(n) = 2*a(n-1) + A160552(n). Example: a(6) = 87 = 2*41 + 5, where 5 = A160552(6). %Y A160704 Cf. A139251, A160552, A139250, A001045 %K A160704 nonn %O A160704 1,2 %A A160704 _Gary W. Adamson_, May 24 2009