A094968 Indices of Fibonacci numbers in Stern's diatomic series A049456 regarded as a single linear sequence.

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

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