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A015459 q-Fibonacci numbers for q=2. 6
0, 1, 1, 3, 7, 31, 143, 1135, 10287, 155567, 2789039, 82439343, 2938415279, 171774189743, 12207523172527, 1419381685547183, 201427441344229551, 46711726513354322095, 13247460522448782176431 (list; graph; refs; listen; history; internal format)
OFFSET

0,4

COMMENTS

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 17 2009: (Start)

Preface the series with another "1": (1, 1, 1, 3, 7,...a(n)). Then a(n+2) =

(1, 1, 1, 3, 7,...a(n)) dot (equal number of terms in (1, 2, 4, 8,...)).

Example: (143) = (1, 1, 1, 3, 7) dot (1, 2, 4, 8, 16) = (1 + 2 + 4 + 24 + 112).

Analogous procedures apply to other q-Fibonacci sequences for q(n). (End)

FORMULA

a(n) = a(n-1) + 2^(n-2) a(n-2).

Associated constant: C_2=lim n ->infty a(n)*a(n-2)/a(n-1)^2 =1.225306147422043724739386133....(C_1=1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 30 2003

CROSSREFS

Cf. A015460.

Sequence in context: A121620 A042271 A000644 * A115083 A141385 A059296

Adjacent sequences:  A015456 A015457 A015458 * A015460 A015461 A015462

KEYWORD

nonn,easy

AUTHOR

Olivier Gerard (olivier.gerard(AT)gmail.com)

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Last modified February 14 18:09 EST 2012. Contains 205663 sequences.