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A301848 Number of states generated by morphism during inflation stage of paper-folding sequence. 4
1, 3, 1, 4, 1, 3, 2, 4, 1, 3, 1, 4, 2, 3, 2, 4, 1, 3, 1, 4, 1, 3, 2, 4, 2, 3, 1, 4, 2, 3, 2, 4, 1, 3, 1, 4, 1, 3, 2, 4, 1, 3, 1, 4, 2, 3, 2, 4, 2, 3, 1, 4, 1, 3, 2, 4, 2, 3, 1, 4, 2, 3, 2, 4, 1, 3, 1, 4, 1, 3, 2, 4, 1, 3, 1, 4, 2, 3, 2, 4, 1, 3, 1, 4, 1, 3, 2, 4, 2, 3, 1, 4, 2, 3, 2, 4, 2, 3, 1, 4, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(0), a(1), ... is the fixed point of inflation morphism 1 -> 1 3, 2 -> 2 3, 3 -> 1 4, 4 -> 2 4, starting from state 1;

b(0), b(1), ... is the image of a(n) under encoding morphism 1 -> 0, 2 -> 1, 3 -> 0, 4 -> 1.

The number-wall over the rationals (signed Hankel determinants) is apparently free from zeros.

REFERENCES

Jean-Paul Allouche and Jeffrey O. Shallit, Automatic sequences, Cambridge, 2003, sect. 5.1.6.

LINKS

Table of n, a(n) for n=0..100.

W. F. Lunnon, The number-wall algorithm: an LFSR cookbook, Journal of Integer Sequences 4 (2001), no. 1, 01.1.1.

FORMULA

a(n) = b(2n) - 2 b(2n-1) + 3, where b(n) denotes A038189(n).

MAPLE

A301848 := proc(n)

    A038189(2*n)-2*A038189(2*n-1)+3 ;

end proc:

seq(A301848(n), n=0..100) ; # R. J. Mathar, Mar 30 2018

PROG

(Magma)

function b (n)

  if n eq 0 then return 0; // alternatively,  return 1;

  else while IsEven(n) do n := n div 2; end while; end if;

  return n div 2 mod 2; end function;

function a (n)

  return b(n+n) - 2*b(n+n-1) + 3; end function;

  nlo := 0; nhi := 32;

  [a(n) : n in [nlo..nhi] ];

CROSSREFS

Cf. A038189, A301849, A301850.

Sequence in context: A094603 A165595 A213181 * A325610 A278536 A143825

Adjacent sequences:  A301845 A301846 A301847 * A301849 A301850 A301851

KEYWORD

nonn

AUTHOR

Fred Lunnon, Mar 27 2018

STATUS

approved

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Last modified June 21 19:59 EDT 2021. Contains 345365 sequences. (Running on oeis4.)