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 A265283 Number of ON (black) cells in the n-th iteration of the "Rule 94" elementary cellular automaton starting with a single ON (black) cell. 6
 1, 3, 4, 6, 6, 8, 8, 10, 10, 12, 12, 14, 14, 16, 16, 18, 18, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40, 42, 42, 44, 44, 46, 46, 48, 48, 50, 50, 52, 52, 54, 54, 56, 56, 58, 58, 60, 60, 62, 62, 64, 64, 66, 66, 68 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From Gus Wiseman, Apr 13 2019: (Start) Also the number of integer partitions of n + 3 such that lesser of the maximum part and the number of parts is 2. The Heinz numbers of these partitions are given by A325229. For example, the a(0) = 1 through a(7) = 10 partitions are:   (21)  (22)   (32)    (33)     (43)      (44)       (54)        (55)         (31)   (41)    (42)     (52)      (53)       (63)        (64)         (211)  (221)   (51)     (61)      (62)       (72)        (73)                (2111)  (222)    (2221)    (71)       (81)        (82)                        (2211)   (22111)   (2222)     (22221)     (91)                        (21111)  (211111)  (22211)    (222111)    (22222)                                           (221111)   (2211111)   (222211)                                           (2111111)  (21111111)  (2221111)                                                                  (22111111)                                                                  (211111111) (End) REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. LINKS Robert Price, Table of n, a(n) for n = 0..999 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton FORMULA Conjectures from Colin Barker, Dec 07 2015 and Apr 16 2019: (Start) a(n) = (5-(-1)^n+2*n)/2 = A213222(n+3) for n>1. a(n) = n+2 for n>1 and even. a(n) = n+3 for n>1 and odd. a(n) = a(n-1) + a(n-2) - a(n-3) for n>2. G.f.: (1+2*x-x^4) / ((1-x)^2*(1+x)). (End) EXAMPLE From Michael De Vlieger, Dec 14 2015: (Start) First 12 rows, replacing "0" with "." for better visibility of ON cells, followed by the total number of 1's per row:                         1                          =  1                       1 1 1                        =  3                     1 1 . 1 1                      =  4                   1 1 1 . 1 1 1                    =  6                 1 1 . 1 . 1 . 1 1                  =  6               1 1 1 . 1 . 1 . 1 1 1                =  8             1 1 . 1 . 1 . 1 . 1 . 1 1              =  8           1 1 1 . 1 . 1 . 1 . 1 . 1 1 1            = 10         1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1          = 10       1 1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1 1        = 12     1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1      = 12   1 1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1 1    = 14 1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1  = 14 (End) MATHEMATICA rule = 94; rows = 30; Table[Total[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]]], {k, 1, rows}] Total /@ CellularAutomaton[94, {{1}, 0}, 65] (* Michael De Vlieger, Dec 14 2015 *) CROSSREFS Column k = 2 of A325227. Cf. A004526, A051924, A118102, A263297, A325193, A325225, A325228, A325229, A325232. Sequence in context: A325611 A263842 A286956 * A023836 A064800 A078574 Adjacent sequences:  A265280 A265281 A265282 * A265284 A265285 A265286 KEYWORD nonn,easy AUTHOR Robert Price, Dec 06 2015 STATUS approved

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