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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.)