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 A186411 #23 Aug 01 2023 06:54:58 %S A186411 0,1,5,5,21,5,21,21,101,5,21,21,101,21,101,101,501,5,21,21,101,21,101, %T A186411 101,501,21,101,101,501,101,501,501,2501,5,21,21,101,21,101,101,501, %U A186411 21,101,101,501,101,501,501,2501,21,101,101,501,101,501,501,2501,101 %N A186411 First differences of A186410. %C A186411 Number of cells turned "ON" at h-th stage of the three-dimensional cellular automaton of A186410. In other words: number of cubes added at n-th stage to the structure of A186410. %H A186411 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 A186411 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 A186411 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>. %F A186411 a(n) = 1 + 4*5^(A000120(n-1)-1), n >= 2. - _Nathaniel Johnston_, Mar 22 2011 %t A186411 a[n_] := 1 + 4*5^(DigitCount[n-1, 2, 1]-1); a[0] = 0; a[1] = 1; Array[a, 100, 0] (* _Amiram Eldar_, Aug 01 2023 *) %Y A186411 Cf. A000120, A147582, A151779, A186410. %K A186411 nonn %O A186411 0,3 %A A186411 _Omar E. Pol_, Feb 21 2011 %E A186411 More terms from _Nathaniel Johnston_, Mar 22 2011 %E A186411 More terms from _Amiram Eldar_, Aug 01 2023