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A108336 Unique sequence of 1's and 0's such that (Sum_{n >= 0} a(n)*x^n)^2 mod 4 has coefficients which are all 1's and 2's (A083952). 6
1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Equals A084202 read mod 2.

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006.

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

MAPLE

S:= 0: SS:= 0:

for i from 0 to 100 do

  s:= coeff(SS, x, i);

  if s = 0 or s = 3 then

     SS:= SS + 2*expand(S*x^i)+x^(2*i) mod 4; S:= S + x^i;

  fi

od:

seq(coeff(S, x, i), i=0..100); # Robert Israel, May 14 2019

MATHEMATICA

max = 98; (* a = A084202 *) a[n_] := a[n] = Block[{s = Sum[a[i]*x^i, {i, 0, n-1}]}, If[IntegerQ @ Last @ CoefficientList[Series[Sqrt[s + x^n], {x, 0, n}], x], 1, 2]]; Table[a[n], {n, 0, max}]; A108336 = CoefficientList[ Series[Sqrt[Sum[a[i]*x^i, {i, 0, max}]], {x, 0, max}], x] // Mod[#, 2]& (* Jean-François Alcover, Apr 01 2016, after Robert G. Wilson v *)

CROSSREFS

Cf. A083952, A084202, A108335, A108337, A108340.

Sequence in context: A093075 A104120 A254634 * A279733 A176723 A189126

Adjacent sequences:  A108333 A108334 A108335 * A108337 A108338 A108339

KEYWORD

nonn,easy,nice,changed

AUTHOR

N. J. A. Sloane and Nadia Heninger, Jul 02 2005

STATUS

approved

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Last modified May 26 02:35 EDT 2019. Contains 323579 sequences. (Running on oeis4.)