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A094968 Indices of Fibonacci numbers in Stern's diatomic series A049456 regarded as a single linear sequence. 1
1, 4, 7, 14, 25, 48, 91, 178, 349, 692, 1375, 2742, 5473, 10936, 21859, 43706, 87397, 174780, 349543, 699070, 1398121, 2796224, 5592427, 11184834, 22369645, 44739268, 89478511, 178956998, 357913969, 715827912, 1431655795, 2863311562 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

By definition, A049456(a(n))=Fib(n+2).

The rank of Fib(n+2) in row n of A049456 (regarded as an irregular triangle read by rows) is A128209(n) = A001045(n)+1. [Comment edited by N. J. A. Sloane, Nov 23 2016]

LINKS

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

D. H. Lehmer, On Stern's Diatomic Series, Amer. Math. Monthly 36(1) 1929, pp. 59-67.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).

FORMULA

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

a(n) = 2^n + n + Jacobsthal(n).

a(n) = A006127(n) + A001045(n).

From Colin Barker, Sep 29 2017: (Start)

a(n) = ((-1)^(1+n) + 2^(2+n) + 3*n) / 3.

a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4) for n>3.

(End)

PROG

(PARI) Vec((1 + x - 4*x^2) / ((1 - x)^2*(1 + x)*(1 - 2*x)) + O(x^30)) \\ Colin Barker, Sep 29 2017

CROSSREFS

Cf. A000045, A001045, A049456, A128209.

Sequence in context: A221107 A128610 A305124 * A049946 A076975 A050343

Adjacent sequences:  A094965 A094966 A094967 * A094969 A094970 A094971

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 26 2004

STATUS

approved

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Last modified September 24 07:34 EDT 2021. Contains 347623 sequences. (Running on oeis4.)