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Search: id:A094967
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| A094967 |
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Right-hand neighbors of Fibonacci numbers in Stern's diatomic series. |
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+0
4
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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; listen)
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OFFSET
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0,3
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COMMENT
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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)=A0994966(n)+a(n).
Diagonal sums of A109223. - Paul Barry (pbarry(AT)wit.ie), Jun 22 2005
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FORMULA
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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
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CROSSREFS
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Cf. A001519.
Cf. A133080.
Sequence in context: A030223 A056504 A122205 this_sequence A056505 A056506 A056507
Adjacent sequences: A094964 A094965 A094966 this_sequence A094968 A094969 A094970
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 26 2004
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