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 A265056 #23 Sep 04 2025 22:55:32
%S A265056 1,5,21,45,77,117,165,221,285,357,437,525,621,725,837,957,1085,1221,
%T A265056 1365,1517,1677,1845,2021,2205,2397,2597,2805,3021,3245,3477,3717,
%U A265056 3965,4221,4485,4757,5037,5325,5621,5925,6237,6557,6885,7221,7565,7917,8277,8645,9021,9405,9797,10197,10605,11021
%N A265056 Partial sums of A234275.
%C A265056 The number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 899", based on the 5-celled von Neumann neighborhood, initiated with a single black (ON) cell. - _Robert Price_, May 28 2016
%C A265056 For n > 0, a(n) is the number of unit squares visible when two (2n-1) X (2n+1) grids are placed perpendicular to each other with their centers aligned. - _Kiran Ananthpur Bacche_, Sep 04 2025
%D A265056 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A265056 Colin Barker, <a href="/A265056/b265056.txt">Table of n, a(n) for n = 0..1000</a>
%H A265056 N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015
%H A265056 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A265056 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A265056 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A265056 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A265056 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A265056 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A265056 From _Colin Barker_, Jan 01 2016: (Start)
%F A265056 a(n) = 4*n^2+4*n-3 for n>0.
%F A265056 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>3.
%F A265056 G.f.: (1+2*x+9*x^2-4*x^3) / (1-x)^3.
%F A265056 (End)
%t A265056 Accumulate[LinearRecurrence[{2,-1},{1,4,16,24},60]] (* or *) LinearRecurrence[{3,-3,1},{1,5,21,45},60] (* _Harvey P. Dale_, Sep 22 2024 *)
%o A265056 (PARI) Vec((1+2*x+9*x^2-4*x^3)/(1-x)^3 + O(x^100)) \\ _Colin Barker_, Jan 01 2016
%Y A265056 Cf. A234275.
%Y A265056 Apart from initial term, same as A078371.
%K A265056 nonn,easy,changed
%O A265056 0,2
%A A265056 _N. J. A. Sloane_, Dec 28 2015