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A192304 0-sequence of reduction of (2n-1) by x^2 -> x+1. 3
1, 1, 6, 13, 31, 64, 129, 249, 470, 869, 1583, 2848, 5073, 8961, 15718, 27405, 47535, 82080, 141169, 241945, 413366, 704261, 1196831, 2029248, 3433441, 5798209, 9774534, 16451149, 27646975, 46397824 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".

LINKS

Table of n, a(n) for n=1..30.

FORMULA

Empirical G.f.: x*(1-2*x+4*x^2-x^3)/(1-3*x+x^2+3*x^3-x^4-x^5). [Colin Barker, Feb 08 2012]

MATHEMATICA

c[n_] := 2 n - 1; (* odd numbers, A005408 *)

Table[c[n], {n, 1, 15}]

q[x_] := x + 1;

p[0, x_] := 1; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1]

reductionRules = {x^y_?EvenQ -> q[x]^(y/2),

   x^y_?OddQ -> x q[x]^((y - 1)/2)};

t = Table[

  Last[Most[

    FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,

   30}]

Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}]  (* A192304  *)

Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A178525 *)

(* by Peter J. C. Moses, Jun 20 2011 *)

CROSSREFS

Cf. A192232, A178525.

Sequence in context: A145976 A101622 A256871 * A147330 A042607 A048693

Adjacent sequences:  A192301 A192302 A192303 * A192305 A192306 A192307

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 27 2011

STATUS

approved

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Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)