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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210729 a(n) = a(n-1)+a(n-2)+n+3 with n>1, a(0)=1, a(1)=2. 2
1, 2, 8, 16, 31, 55, 95, 160, 266, 438, 717, 1169, 1901, 3086, 5004, 8108, 13131, 21259, 34411, 55692, 90126, 145842, 235993, 381861, 617881, 999770, 1617680, 2617480, 4235191, 6852703, 11087927, 17940664, 29028626, 46969326, 75997989, 122967353 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).

FORMULA

G.f.: (1-x+4*x^2-3*x^3)/((1-x-x^2)*(1-x)^2).

a(n) = 3*Fibonacci(n+1)+2*Fibonacci(n+3)-n-6. - Vaclav Kotesovec, May 13 2012

MATHEMATICA

Table[3*Fibonacci[n+1]+2*Fibonacci[n+3]-n-6, {n, 0, 35}] (* Vaclav Kotesovec, May 13 2012 *)

PROG

(Python)

prpr, prev = 1, 2

for n in range(2, 99):

    current = prev+prpr+n+3

    print prpr,

    prpr = prev

    prev = current

(MAGMA) [3*Fibonacci(n+1)+2*Fibonacci(n+3)-n-6: n in [0..40]]; // Vincenzo Librandi, Jul 18 2013

CROSSREFS

Cf. A065220: a(n)=a(n-1)+a(n-2)+n-5, a(0)=1,a(1)=2 (except first 2 terms).

Cf. A168043: a(n)=a(n-1)+a(n-2)+n-3, a(0)=1,a(1)=2 (except first 2 terms).

Cf. A131269: a(n)=a(n-1)+a(n-2)+n-2, a(0)=1,a(1)=2.

Cf. A000126: a(n)=a(n-1)+a(n-2)+n-1, a(0)=1,a(1)=2.

Cf. A104161: a(n)=a(n-1)+a(n-2)+n,   a(0)=1,a(1)=2 (except the first term).

Cf. A192969: a(n)=a(n-1)+a(n-2)+n+1, a(0)=1,a(1)=2.

Cf. A210728: a(n)=a(n-1)+a(n-2)+n+2, a(0)=1,a(1)=2.

Sequence in context: A136514 A077071 A187216 * A294534 A294542 A294553

Adjacent sequences:  A210726 A210727 A210728 * A210730 A210731 A210732

KEYWORD

nonn,easy

AUTHOR

Alex Ratushnyak, May 10 2012

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 June 17 16:56 EDT 2019. Contains 324196 sequences. (Running on oeis4.)