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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080926 Partial sums of A080925. 7
0, 1, 6, 19, 60, 181, 546, 1639, 4920, 14761, 44286, 132859, 398580, 1195741, 3587226, 10761679, 32285040, 96855121, 290565366, 871696099, 2615088300, 7845264901, 23535794706, 70607384119, 211822152360, 635466457081 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This is the sequence A(0,1;2,3;4) of the family of sequences [a,b:c,d:k] considered by G. Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. [Wolfdieter Lang, Oct 18 2010]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Wolfdieter Lang, Notes on certain inhomogeneous three term recurrences. [Wolfdieter Lang, Oct 18 2010]

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

FORMULA

a(n) = Sum{i=0..n, Sum{k=1..i, Binomial(i, 2k-2)2^(2k-2)}}

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

E.g.f.: (3*exp(3x)+exp(-x))/4-exp(x).

a(n) = (3*3^n+(-1)^n)/4-1.

a(n) = 3*a(n-1) + a(n-2) - 3*a(n-3) for n>2, a(0)=0, a(1)=1, a(2)=6. Observation by G. Detlefs. See my comment and link. [Wolfdieter Lang, Oct 18 2010]

MAPLE

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]+3*a[n-2]+4 od: seq(a[n], n=0..33); # Zerinvary Lajos, Dec 14 2008

MATHEMATICA

CoefficientList[Series[x (1 + 3 x) / ((1 + x) (1 - x) (1 - 3 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)

LinearRecurrence[{3, 1, -3}, {0, 1, 6}, 30] (* Harvey P. Dale, Oct 02 2018 *)

PROG

(MAGMA) [(3*3^n+(-1)^n)/4-1: n in [0..30]]; // Vincenzo Librandi, Aug 06 2013

CROSSREFS

Sequence in context: A272227 A272587 A125069 * A184189 A152098 A041673

Adjacent sequences:  A080923 A080924 A080925 * A080927 A080928 A080929

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Feb 26 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 July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)