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A192068 a(n) = Fibonacci(2*n) - n mod 2. 3
0, 3, 7, 21, 54, 144, 376, 987, 2583, 6765, 17710, 46368, 121392, 317811, 832039, 2178309, 5702886, 14930352, 39088168, 102334155, 267914295, 701408733, 1836311902, 4807526976, 12586269024, 32951280099, 86267571271, 225851433717, 591286729878 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Previous name was: 1-sequence of reduction of Lucas sequence by x^2 -> x+1.

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

LINKS

Table of n, a(n) for n=1..29.

FORMULA

Empirical G.f. and recurrence: x^2*(3-2*x)/(1-3*x+3*x^3-x^4), a(n)=3*a(n-1)-3*a(n-3)+a(n-4). - Colin Barker, Feb 08 2012

a(n) = Fibonacci(2*n) - (n mod 2). - Peter Luschny, Mar 10 2015

EXAMPLE

(See A192243.)

MAPLE

a := n -> combinat[fibonacci](2*n)-(n mod 2):

seq(a(n), n=1..29); # Peter Luschny, Mar 10 2015

MATHEMATICA

c[n_] := LucasL[n];

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}]  (* A192243 *)

Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A192068 *)

(* by Peter J. C. Moses, Jun 26 2011 *)

CROSSREFS

Cf. A000032, A000045, A192243, A192068.

Sequence in context: A018303 A098545 A161707 * A318395 A151267 A319558

Adjacent sequences:  A192065 A192066 A192067 * A192069 A192070 A192071

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 26 2011

EXTENSIONS

New name from Peter Luschny, Mar 10 2015

STATUS

approved

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Last modified February 22 14:19 EST 2020. Contains 332136 sequences. (Running on oeis4.)