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 A151907 #15 Feb 24 2021 02:48:18 %S A151907 0,1,5,9,13,25,29,33,45,57,69,105,109,113,125,137,149,185,197,209,245, %T A151907 281,317,425,429,433,445,457,469,505,517,529,565,601,637,745,757,769, %U A151907 805,841,877,985,1021,1057,1165,1273,1381,1705,1709,1713,1725,1737,1749,1785,1797 %N A151907 Partial sums of A151906. %C A151907 a(n) is the total number of ON cells after n generations in the Holladay-Ulam CA shown in Fig. 2 and Example 2 of the Ulam article. %C A151907 The definition of this CA given by Ulam on pp. 216, 222 is complicated (and incomplete). However, the same structure can be obtained as follows. Take the CA of A147562 but replace each square by a Maltese cross, a cluster of five adjacent squares: %C A151907 ..X.. %C A151907 .XXX. %C A151907 ..X.. %C A151907 We guess that this was how Holladay and Ulam originally constructed the CA. %C A151907 This construction corresponds to the fact that the three trisections of the difference sequence A151906 are essentially A147582, A147582 and 3*A147582 respectively. %D A151907 S. Ulam, On some mathematical problems connected with patterns of growth of figures, pp. 215-224 of R. E. Bellman, ed., Mathematical Problems in the Biological Sciences, Proc. Sympos. Applied Math., Vol. 14, Amer. Math. Soc., 1962. %H A151907 David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a> %H A151907 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 A151907 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 A151907 N. J. A. Sloane, <a href="/A151907/a151907.jpg">Illustration of initial terms</a> (annotated copy of figure on p. 222 of Ulam) %F A151907 The definition in terms of A151906 provides an explicit formula for a(n). %Y A151907 Cf. A151904, A151905, A151906, A139250, A151895, A151896. %K A151907 nonn %O A151907 0,3 %A A151907 _David Applegate_ and _N. J. A. Sloane_, Jul 31 2009, Aug 03 2009