The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 16 20:53 EDT 2024. Contains 375977 sequences. (Running on oeis4.)