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A094967
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Right-hand neighbors of Fibonacci numbers in Stern's diatomic series.
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8
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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; internal format)
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OFFSET
| 0,3
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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 (pbarry(AT)wit.ie), 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]
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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 (pbarry(AT)wit.ie), Jun 22 2005
Starting (1, 2, 2, 5, 5, 13, 13,...) = A133080 * A000045, where A000045 starts with "1". - Gary W. Adamson (qntmpkt(AT)yahoo.com), 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]
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MAPLE
| A094967 := proc(n) combinat[fibonacci](2*floor(n/2)+1) ; end proc: seq(A094967(n), n=0..37);
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CROSSREFS
| Cf. A001519, A133080.
Sequence in context: A056504 A122205 A178115 * A056505 A056506 A056507
Adjacent sequences: A094964 A094965 A094966 * A094968 A094969 A094970
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 26 2004
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