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A190018 Union of A000045, A007598, and A059929. 2
0, 1, 2, 3, 4, 5, 8, 9, 10, 13, 21, 24, 25, 34, 55, 64, 65, 89, 144, 168, 169, 233, 377, 441, 442, 610, 987, 1155, 1156, 1597, 2584, 3025, 3026, 4181, 6765, 7920, 7921, 10946, 17711, 20736, 20737, 28657, 46368, 54288, 54289, 75025, 121393, 142129, 142130 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Each term is F(k) or F(k)^2 or F(k-1)*F(k+1) for appropriate k, F=A000045, the Fibonacci numbers.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: -x*(x^16+2*x^15+4*x^14 +5*x^13+3*x^12+x^11 -4*x^10-7*x^9-10*x^8 -12*x^7-14*x^6-14*x^5 -12*x^4-10*x^3-6*x^2-3*x-1) / ((x+1)*(x^2+1)*(x^4+1)*(x^4+x^2-1)*(x^4-x^2-1)). - Alois P. Heinz, May 05 2011

EXAMPLE

a(10) = F(8) = 21;

a(11) = F(4) * F(6) = 3 * 8 = 24;

a(12) = F(5)^2 = 5^2 = 25;

a(13) = F(9) = 34;

a(14) = F(10) = 55;

a(15) = F(6)^2 = 8^2 = 64;

a(16) = F(5) * F(7) = 5 * 13 = 65;

a(17) = F(11) = 89;

a(18) = F(12) = 144;

a(19) = F(6) * F(8) = 8 * 21 = 168;

a(20) = F(7)^2 = 13^2 = 169.

MAPLE

a:= n-> `if`(n<6, n, (Matrix(15, (i, j)-> `if`(j=i+1, 1, `if`(i=15, [-1$4, 2$8, -1$3][j], 0)))^n. <<0, 1, 1, 0, 0, [1$4][], 2, 2, 3, 3, 4, 5>>)[10, 1]): seq(a(n), n=0..50);  # Alois P. Heinz, May 04 2011

MATHEMATICA

CoefficientList[Series[-x*(x^16+2*x^15+4*x^14 +5*x^13+3*x^12+x^11 -4*x^10 -7*x^9-10*x^8 -12*x^7-14*x^6-14*x^5 -12*x^4-10*x^3-6*x^2-3*x-1)/((x+1)*(x^2+1)*(x^4+1)*(x^4+x^2-1)*(x^4-x^2-1)), {x, 0, 50}], x] (* G. C. Greubel, Jan 11 2018 *)

PROG

(Haskell)

a190018 n = a190018_list !! n

a190018_list = 0 : drop 2 (merge (merge fibs $

    map (^ 2) fibs) $ zipWith (*) fibs (drop 2 fibs))

    where fibs = 0 : 1 : zipWith (+) fibs (tail fibs)

          merge xs'@(x:xs) ys'@(y:ys)

             | x < y     = x : merge xs ys'

             | x == y    = x : merge xs ys

             | otherwise = y : merge xs' ys

(PARI) x='x+O('x^50); concat([0], Vec(-x*(x^16+2*x^15+4*x^14 +5*x^13 +3*x^12+x^11 -4*x^10-7*x^9-10*x^8 -12*x^7-14*x^6-14*x^5 -12*x^4-10*x^3 -6*x^2-3*x-1)/((x+1)*(x^2+1)*(x^4+1)*(x^4+x^2-1)*(x^4-x^2-1)))) \\ G. C. Greubel, Jan 11 2018

CROSSREFS

Sequence in context: A102471 A243490 A094566 * A217349 A087278 A054219

Adjacent sequences:  A190015 A190016 A190017 * A190019 A190020 A190021

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 04 2011

STATUS

approved

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Last modified February 15 16:53 EST 2019. Contains 320136 sequences. (Running on oeis4.)