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A207191 Numbers that match even polynomials among the monic polynomials over {-1,0,1}, ordered as at A206821. 3
1, 4, 5, 8, 26, 27, 30, 31, 42, 45, 46, 120, 121, 124, 125, 136, 137, 140, 141, 184, 187, 188, 199, 200, 203, 204, 502, 503, 506, 507, 518, 519, 522, 523, 566, 567, 570, 571, 582, 583, 586, 587, 758, 761, 762, 773, 774, 777, 778, 821, 822, 825, 826 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The polynomials y(k,x) range through all monic polynomials with coefficients in {-1,0,1}, ordered as at A206821.

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

The first 13 polynomials:

1 .... 1

2 .... x

3 .... x + 1

4 .... x^2

5 .... x^2 - 1

6 .... x^2 - x

7 .... x^2 - x - 1

8 .... x^2 + 1

9 .... x^2 + x

10 ... x^2 + x + 1

11 ... x^3

12 ... x^3 - 1

13 ... x^3 - x

Numbers n for which y(n,-x)=y(n,x): 1,4,5,8,26,...

Numbers n for which y(n,-x)=-y(n,x): 2,11,13,20,...

MATHEMATICA

t = Table[IntegerDigits[n, 2], {n, 1, 2000}];

b[n_] := Reverse[Table[x^k, {k, 0, n}]]

p[n_] := p[n] = t[[n]].b[-1 + Length[t[[n]]]]

TableForm[Table[{n, p[n], Factor[p[n]]}, {n, 1, 6}]]

f[k_] := 2^k - k; g[k_] := 2^k - 2 + f[k - 1];

q1[n_] := p[2^(k - 1)] - p[n + 1 - f[k]]

q2[n_] := p[n - f[k] + 2]

y1 = Table[p[n], {n, 1, 4}];

Do[AppendTo[y1,

  Join[Table[q1[n], {n, f[k], g[k] - 1}],

   Table[q2[n], {n, g[k], f[k + 1] - 1}]]], {k, 3, 10}]

y = Flatten[y1]; (* polynomials over {-1, 0, 1} *)

Flatten[Position[y - (y /. x -> -x), 0]]  (* A207191 *)

Flatten[Position[y + (y /. x -> -x), 0]]  (* A207192  *)

CROSSREFS

Cf. A206821.

Sequence in context: A104884 A226795 A113726 * A240790 A229861 A140315

Adjacent sequences:  A207188 A207189 A207190 * A207192 A207193 A207194

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 16 2012

STATUS

approved

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Last modified April 22 08:56 EDT 2019. Contains 322329 sequences. (Running on oeis4.)