login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099485 A Fibonacci convolution. 2
1, 2, 5, 14, 37, 96, 251, 658, 1723, 4510, 11807, 30912, 80929, 211874, 554693, 1452206, 3801925, 9953568, 26058779, 68222770, 178609531, 467605822, 1224207935, 3205017984, 8390846017, 21967520066, 57511714181, 150567622478 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A Chebyshev transform of A025192 with g.f. (1-x)/(1-3x). The image of G(x) under the Chebyshev transform is (1/(1+x^2))G(x/(1+x^2)).

LINKS

Table of n, a(n) for n=0..27.

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

FORMULA

G.f.: (1-x+x^2)/((1+x^2)(1-3x+x^2)); a(n)=3a(n-1)-2a(n-2)+3a(n-3); a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^n*(2*3^(n-2k)+0^(n-2k))/3}; a(n)=sum{k=0..n, (0^k-sin(pi*k/2))F(2(n-k)+2)}.

(1/6) [4Fib(2n+2) + I^n + (-I)^n ]. - Ralf Stephan, Dec 04 2004

Also a transformation of the Jacobsthal numbers A001045(n+1) under the mapping G(x)-> (1/(1-x+x^2))G(x/(1-x+x^2)). - Paul Barry, Dec 11 2004

MATHEMATICA

LinearRecurrence[{3, -2, 3, -1}, {1, 2, 5, 14}, 30] (* Harvey P. Dale, Jul 06 2017 *)

CROSSREFS

Cf. A000045, A099483, A099484.

Sequence in context: A062197 A030016 A248733 * A038990 A077938 A077987

Adjacent sequences:  A099482 A099483 A099484 * A099486 A099487 A099488

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 18 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 22 05:55 EST 2019. Contains 329388 sequences. (Running on oeis4.)