login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A083217 (2*5^n+(-1)^n)/3. 1
1, 3, 17, 83, 417, 2083, 10417, 52083, 260417, 1302083, 6510417, 32552083, 162760417, 813802083, 4069010417, 20345052083, 101725260417, 508626302083, 2543131510417, 12715657552083, 63578287760417, 317891438802083 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A003683 (without leading zero). Inverse binomial transform of A067411.

a(n) is the number of compositions of n when there are 3 types of 1 and 8 types of other natural numbers. - Milan Janjic, Aug 13 2010

LINKS

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (4,5).

FORMULA

a(n)=(2*5^n+(-1)^n)/3. G.f.: (1-x)/((1-5x)(1+x)). E.g.f.: (2exp(5x) + exp(-x))/3

a(n)=sum{k=0..n, sum{j=0..n-k, C(n,j)C(n-j,k)J(n-j+1)}} where J(n)=A001045(n); - Paul Barry, May 19 2006

a(0)=1, a(n)=5*a(n-1)-2 if n is odd; a(n)=5*a(n)+2 if n is even. - Vincenzo Librandi, Nov 18 2010

MATHEMATICA

LinearRecurrence[{4, 5}, {1, 3}, 30] (* Harvey P. Dale, Sep 18 2018 *)

PROG

(Sage) from sage.combinat.sloane_functions import recur_gen2b; it = recur_gen2b(1, 3, 4, 5, lambda n: 0); [it.next() for i in range(1, 24)] # Zerinvary Lajos, Jul 03 2008

CROSSREFS

Cf. A082412.

Sequence in context: A225342 A194596 A217623 * A225307 A318769 A216681

Adjacent sequences:  A083214 A083215 A083216 * A083218 A083219 A083220

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 23 2003

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 February 26 01:28 EST 2020. Contains 332270 sequences. (Running on oeis4.)