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 A160128 #26 Feb 24 2021 02:48:18 %S A160128 3,7,19,63,235,919,3651,14575,58267,233031,932083,3728287,14913099, %T A160128 59652343,238609315,954437199,3817748731,15270994855,61083979347, %U A160128 244335917311,977343669163,3909374676567,15637498706179 %N A160128 a(n) = number of grid points that are covered after (2^n)th stage of A139250. %H A160128 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 A160128 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 A160128 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4). %F A160128 a(n) = A147614(A000079(n)). %F A160128 a(n) = (1/9)*(2^(2*n+3) + 12*n + 19). [_Nathaniel Johnston_, Mar 29 2011] %F A160128 It appears that a(n) = A139252(2^(n+1)). - _Omar E. Pol_, Sep 11 2012 %F A160128 a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3). - _Paul Curtz_, May 07 2020 %F A160128 G.f.: (3 - 11*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)). - _Colin Barker_, May 13 2020 %o A160128 (PARI) Vec((3 - 11*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)) + O(x^40)) \\ _Colin Barker_, May 13 2020 %Y A160128 Cf. A000079, A007583, A139250, A139251, A139252, A139560, A147614. %Y A160128 Cf. Same recurrence: A073724, A210985, A014825. %K A160128 nonn,easy %O A160128 0,1 %A A160128 _Omar E. Pol_, May 09 2009 %E A160128 Terms after a(10) from _Nathaniel Johnston_, Mar 29 2011