|
| |
|
|
A022086
|
|
Fibonacci sequence beginning 0 3.
|
|
14
|
|
|
|
0, 3, 3, 6, 9, 15, 24, 39, 63, 102, 165, 267, 432, 699, 1131, 1830, 2961, 4791, 7752, 12543, 20295, 32838, 53133, 85971, 139104, 225075, 364179, 589254, 953433, 1542687, 2496120, 4038807, 6534927, 10573734, 17108661, 27682395, 44791056, 72473451, 117264507
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Pisano period lengths: 1, 3, 1, 6, 20, 3, 16, 12, 8, 60, 10, 6, 28, 48, 20, 24, 36, 24, 18, 60... - R. J. Mathar, Aug 10 2012
|
|
|
REFERENCES
|
A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 7,17.
|
|
|
LINKS
|
Table of n, a(n) for n=0..38.
Index entries for sequences related to linear recurrences with constant coefficients, signature (1,1)
Tanya Khovanova, Recursive Sequences
|
|
|
FORMULA
|
a(n) = round( (6phi-3)/5 phi^n ) (works for n>2) - Thomas Baruchel, Sep 08 2004
3*F(n). For n>1, F(n-2) + F(n+2), with F(n) = A000045(n).
a(n) = A119457(n+1,n-1) for n>1. - Reinhard Zumkeller, May 20 2006
First differences of A111314. - Ross La Haye, May 31 2006
G.f.: 3x/(1-x-x^2). [From Philippe DELEHAM, Nov 19 2008]
|
|
|
MAPLE
|
BB := n->if n=0 then 3; > elif n=1 then 0; > else BB(n-2)+BB(n-1); > fi: > L:=[]: for k from 1 to 34 do L:=[op(L), BB(k)]: od: L; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 19 2007
with (combinat):seq(sum((fibonacci(n, 1)), m=1..3), n=0..32); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 19 2008
|
|
|
MATHEMATICA
|
a={}; b=0; c=3; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 9, 1}]; a (Vladimir Orlovsky, Jul 22 2008)
LinearRecurrence[{1, 1}, {3, 3}, {0, 38}] (* Arkadiusz Wesolowski, Aug 17 2012 *)
|
|
|
CROSSREFS
|
Essentially the same as A097135. Cf. A026390, A036999.
Sequence in context: A035528 A050337 * A097135 A167786 A167787 A185957
Adjacent sequences: A022083 A022084 A022085 * A022087 A022088 A022089
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
STATUS
|
approved
|
| |
|
|
