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A094967 Right-hand neighbors of Fibonacci numbers in Stern's diatomic series. 8
1, 1, 2, 2, 5, 5, 13, 13, 34, 34, 89, 89, 233, 233, 610, 610, 1597, 1597, 4181, 4181, 10946, 10946, 28657, 28657, 75025, 75025, 196418, 196418, 514229, 514229, 1346269, 1346269, 3524578, 3524578, 9227465, 9227465, 24157817, 24157817 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Fib(2n+1) repeated. a(n) is the right neighbor of Fib(n+2) in A049456 and A002487 (starts 2,2,5...). A000045(n+2) = A094966(n) + a(n).

Diagonal sums of A109223. - Paul Barry, Jun 22 2005

The Fi2 sums, see A180662, of triangle A065941 equal the terms of this sequence. [Johannes W. Meijer, Aug 11 2011]

a(n) = last term of (n+1)-th row in Wythoff array A003603. [Reinhard Zumkeller, Jan 26 2012]

LINKS

Table of n, a(n) for n=0..37.

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

FORMULA

G.f. : (1+x-x^2-x^3)/(1-3x^2+x^4); a(n)=Fib(n)(1-(-1)^n)/2+Fib(n+1)(1+(-1)^n)/2.

a(n)=sum{k=0..floor(n/2), binomial(floor(n/2)+k, 2k)}; - Paul Barry, Jun 22 2005

Starting (1, 2, 2, 5, 5, 13, 13,...) = A133080 * A000045, where A000045 starts with "1". - Gary W. Adamson, Sep 08 2007

a(n)= Fib(n+1)^(4k+3) mod Fib(n+2), for any k>-1, n>0 [Gary Detlefs, Nov 29 2010]

MAPLE

A094967 := proc(n) combinat[fibonacci](2*floor(n/2)+1) ; end proc: seq(A094967(n), n=0..37);

MATHEMATICA

LinearRecurrence[{0, 3, 0, -1}, {1, 1, 2, 2}, 40] (* Harvey P. Dale, Apr 05 2015 *)

CROSSREFS

Cf. A001519, A133080.

Sequence in context: A056504 A122205 A178115 * A056505 A056506 A056507

Adjacent sequences:  A094964 A094965 A094966 * A094968 A094969 A094970

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 26 2004

STATUS

approved

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Last modified February 19 09:13 EST 2018. Contains 299330 sequences. (Running on oeis4.)