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A094966 Left-hand neighbors of Fibonacci numbers in Stern's diatomic series. 4
0, 1, 1, 3, 3, 8, 8, 21, 21, 55, 55, 144, 144, 377, 377, 987, 987, 2584, 2584, 6765, 6765, 17711, 17711, 46368, 46368, 121393, 121393, 317811, 317811, 832040, 832040, 2178309, 2178309, 5702887, 5702887, 14930352, 14930352, 39088169, 39088169 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Fibonacci(2n) repeated. a(n) is the left neighbor of Fibonacci(n+2) in A002487 and A049456. A000045(n+2) = a(n)+A094967(n).

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).

FORMULA

G.f.: x*(1+x) / (1-3*x^2+x^4).

a(n) = Fibonacci(n)*(1+(-1)^n)/2 + Fibonacci(n+1)*(1-(-1)^n)/2.

a(n) = (2^(-2-n)*((1-sqrt(5))^n*(-3+sqrt(5)) - (-1-sqrt(5))^n*(-1+sqrt(5)) - (-1+sqrt(5))^n - sqrt(5)*(-1+sqrt(5))^n + 3*(1+sqrt(5))^n + sqrt(5)*(1+sqrt(5))^n))/sqrt(5). - Colin Barker, Mar 28 2016

MATHEMATICA

CoefficientList[Series[x (1 + x)/(1 - 3 x^2 + x^4), {x, 0, 38}], x] (* Michael De Vlieger, Mar 28 2016 *)

PROG

(PARI) concat(0, Vec(x*(1+x)/(1-3*x^2+x^4) + O(x^50))) \\ Colin Barker, Mar 28 2016

(MAGMA) [Fibonacci(n)*(1+(-1)^n)/2 + Fibonacci(n+1)*(1-(-1)^n)/2: n in [0..40]]; // Vincenzo Librandi, Mar 29 2016

CROSSREFS

Cf. A001906.

Sequence in context: A138135 A113166 A126872 * A095068 A248696 A021299

Adjacent sequences:  A094963 A094964 A094965 * A094967 A094968 A094969

KEYWORD

easy,less,nonn

AUTHOR

Paul Barry, May 26 2004

STATUS

approved

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Last modified May 31 22:04 EDT 2020. Contains 334756 sequences. (Running on oeis4.)