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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A022096 Fibonacci sequence beginning 1 6. 15
1, 6, 7, 13, 20, 33, 53, 86, 139, 225, 364, 589, 953, 1542, 2495, 4037, 6532, 10569, 17101, 27670, 44771, 72441, 117212, 189653, 306865, 496518, 803383, 1299901, 2103284, 3403185, 5506469, 8909654, 14416123, 23325777, 37741900, 61067677, 98809577, 159877254 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n-1)=sum(P(6;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=5. These are the sums of the SW-NE diagonals in P(6;n,k), the (6,1) Pascal triangle A093563. Observation by Paul Barry, Apr 29 2004. Proof via recursion relations and comparison of inputs. Also sums of SW-NE diagonals in (1,5)-Pascal triangle A096940.

Subsequence of primes: 7, 13, 53, 139, 953, 44771, 189653, 1494692464747, ... - R. J. Mathar, Aug 09 2012

a(n) is the sum of seven consecutive Fibonacci numbers. a(n)=F(n-4)+F(n-3)+F(n-2)+F(n-1)+F(n)+F(n+1)+F(n+2), where F(n)=A000045(n), extended so that F(-1)=1, F(-2)=-1, F(-3)=2, and F(-4)=-3. - Graeme McRae, Apr 24 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

José L. Ramírez, Gustavo N. Rubiano, and Rodrigo de Castro, A Generalization of the Fibonacci Word Fractal and the Fibonacci Snowflake, arXiv preprint arXiv:1212.1368, 2012

J. L. Ramírez, G. N. Rubiano, Properties and Generalizations of the Fibonacci Word Fractal, The Mathematica Journal, Vol. 16 (2014).

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

FORMULA

a(n) = a(n-1) + a(n-2), n>=2, a(0)=1, a(1)=6.

G.f.: (1+5*x)/(1-x-x^2).

Row sums of triangle A131777. - Gary W. Adamson, Jul 14 2007

a(n) = 5*Fibonacci(n+2)-4*Fibonacci(n+1). - Gary Detlefs, Dec 21 2010

a(n) = (2^(-1-n)*((1-sqrt(5))^n*(-11+sqrt(5))+(1+sqrt(5))^n*(11+sqrt(5))))/sqrt(5). - Herbert Kociemba

MATHEMATICA

CoefficientList[Series[(1 + 5 x)/(1 - x - x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 25 2014 *)

PROG

(MAGMA) a0:=1; a1:=6; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]]; // Bruno Berselli, Feb 12 2013

CROSSREFS

a(n) = A101220(5, 0, n+1).

a(n) = A109754(5, n+1).

Cf. A131777.

Sequence in context: A127020 A154662 A070398 * A041175 A041074 A041749

Adjacent sequences:  A022093 A022094 A022095 * A022097 A022098 A022099

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Spelling correction by Jason G. Wurtzel, Aug 22 2010

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 October 24 06:31 EDT 2014. Contains 248502 sequences.