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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A109794 a(2n) = A001906(n+1), a(2n+1) = A002878(n). 2
1, 1, 3, 4, 8, 11, 21, 29, 55, 76, 144, 199, 377, 521, 987, 1364, 2584, 3571, 6765, 9349, 17711, 24476, 46368, 64079, 121393, 167761, 317811, 439204, 832040, 1149851, 2178309, 3010349, 5702887, 7881196, 14930352, 20633239, 39088169 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sequence relates bisections of Lucas and Fibonacci numbers (see also A098149).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index to sequences with linear recurrences with constant coefficients, signature (0,3,0,-1)

FORMULA

G.f.: (1+x+x^3)/((x^2-x-1)*(x^2+x-1)).

a(n) = (3/20*sqrt(5)+3/4)*(1/2+1/2*sqrt(5))^n + (-3/20*sqrt(5)+3/4)*(1/2-1/2 *sqrt(5))^n + (-3/20*sqrt(5)-1/4)*(-1/2+1/2*sqrt(5))^n +(3/20*sqrt(5)-1/4) *(-1/2-1/2*sqrt(5))^n.

a(n) = 3*a(n-2)-a(n-4), n >= 4; a(0) = 1, a(1) = 1, a(2) = 3, a(3) = 4. - Daniel Forgues, May 07 2011

MAPLE

a:= n-> (<<0|1>, <-1|3>>^iquo(n, 2, 'r'). <<1, 3+r>>)[1, 1]:

seq (a(n), n=0..50);  # Alois P. Heinz, May 02 2011

PROG

Floretion Algebra Multiplication Program, FAMP code: 4jesleftforsumseq[ + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e], vesleftforsumseq = A000045, sumtype: (Y[15], *, inty*sum) (internal program code)

CROSSREFS

Cf. A001906, A002878, A098149, A000045, A189761.

Sequence in context: A006167 A137504 A173401 * A034417 A126873 A050316

Adjacent sequences:  A109791 A109792 A109793 * A109795 A109796 A109797

KEYWORD

nonn,easy

AUTHOR

Creighton Dement, Aug 14 2005

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 23 05:04 EST 2014. Contains 249839 sequences.