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A038183
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One-dimensional cellular automaton 'sigma-minus' (Rule 90): 000,001,010,011,100,101,110,111 -> 0,1,0,1,1,0,1,0.
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18
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1, 5, 17, 85, 257, 1285, 4369, 21845, 65537, 327685, 1114129, 5570645, 16843009, 84215045, 286331153, 1431655765, 4294967297, 21474836485, 73014444049, 365072220245, 1103806595329, 5519032976645, 18764712120593, 93823560602965
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Generation n (starting from the generation 0: 1) interpreted as a binary number.
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REFERENCES
| Stephen Wolfram: Geometry of Binomial Coefficients, Amer. Math. Monthly, Volume 91, Number 9, November 1984, pages 566-571.
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LINKS
| Author?, Algebraic Properties of Cellular Automata (1984)
Eric Weisstein's World of Mathematics, Rule 90
Index entries for sequences related to cellular automata
Wikipedia, Rule 90
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FORMULA
| a(n) = Product(((bit_n(n, i)*(2^(2^(i+1))))+1), i=0..inf); # A direct algebraic formula!
a(n)=sum{k=0..n, (C(2n, 2k) mod 2)*4^(n-k)} - Paul Barry (pbarry(AT)wit.ie), Jan 03 2005
a(2n+1) = 5*a(2n); a(n+1) = a(n) XOR 4a(n) where XOR is binary exclusive OR operator . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 18 2005
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MAPLE
| bit_n := (x, n) -> `mod`(floor(x/(2^n)), 2);
A recursive, cellular automaton rule version:
sigmaminus := proc(n) option remember: if (0 = n) then (1)
else sum('((bit_n(sigmaminus(n-1), i)+bit_n(sigmaminus(n-1), i-2)) mod 2)*(2^i)', 'i'=0..(2*n)) fi: end:
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CROSSREFS
| Cf. A006977, A006978, A038184, A038185 (other cellular automata), A000215 (Fermat numbers).
Also alternate terms of A001317. Cf. A048710, A048720, A048757 (same 0/1-patterns interpreted in Fibonacci number system).
Equals 4*A089893(n)+1.
Sequence in context: A149754 A149755 A002020 * A149756 A036756 A149757
Adjacent sequences: A038180 A038181 A038182 * A038184 A038185 A038186
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen, Feb 09 1999
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