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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A121990 Expansion of x*(1+9*x+2*x^2)/((1-x)*(x^2-3*x+1)). 1
1, 13, 50, 149, 409, 1090, 2873, 7541, 19762, 51757, 135521, 354818, 928945, 2432029, 6367154, 16669445, 43641193, 114254146, 299121257, 783109637, 2050207666, 5367513373, 14052332465, 36789484034, 96316119649, 252158874925 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-4,1).

FORMULA

a(n) = 3*a(n - 1) - a(n - 2) + 12.

a(n) = (1/10)*(-120 + (65 - 11*sqrt(5))*((1/2)*(3 - sqrt(5)))^n + ((1/2)*(3 + sqrt(5)))^n*(65 + 11*sqrt(5))).

From R. J. Mathar, Apr 04 2009: (Start)

a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3).

G.f.: x*(1+9*x+2*x^2)/((1-x)*(x^2-3*x+1)). (End)

MATHEMATICA

Join[{1}, RecurrenceTable[{a[n] == 3*a[n - 1] - a[n - 2] + 12, a[1] == 13, a[2] == 50}, a, {n, 1, 49}]] (* or *) LinearRecurrence[{4, -4, 1}, {1, 13, 50}, 50] (* G. C. Greubel, Sep 14 2017 *)

PROG

(PARI) x='x+O('x^50); Vec(x*(1+9*x+2*x^2)/((1-x)*(x^2-3*x+1))) \\ G. C. Greubel, Sep 14 2017

CROSSREFS

Cf. A003215, A005891.

Sequence in context: A209995 A050410 A121991 * A050491 A022283 A135971

Adjacent sequences:  A121987 A121988 A121989 * A121991 A121992 A121993

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Sep 10 2006

EXTENSIONS

Edited and new name based on g.f. by G. C. Greubel and Joerg Arndt, Sep 14 2017

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 21 09:51 EST 2018. Contains 299390 sequences. (Running on oeis4.)