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.

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

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

FindStat, St000533: The maximal number of non-attacking rooks on a Ferrers shape

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

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