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!)
A117917 a(n) = 3*a(n-1) + a(n-2) + n. 1
1, 4, 15, 52, 175, 582, 1927, 6370, 21045, 69514, 229597, 758316, 2504557, 8272000, 27320571, 90233728, 298021771, 984299058, 3250918963, 10737055966, 35462086881, 117123316630, 386832036793, 1277619427032, 4219690317913 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)/a(n-1) tends to 3.30277563... = exp(ArcSinh(3/2)) (A098316).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-6,1,1).

FORMULA

O.g.f.: -(1 - x + x^2)/{(-1+x)^2 (-1 + 3*x + x^2)} . - R. J. Mathar, Mar 17 2008

a(n) = -n/3 - 5/9 + 2*A006190(n)/9 + 14*A006190(n+1)/9. - R. J. Mathar, Oct 21 2012

MATHEMATICA

Join[{a=1, b=4}, Table[c=3*b+a+n; a=b; b=c, {n, 2, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2011 *)

LinearRecurrence[{5, -6, 1, 1}, {1, 4, 15, 52}, 30] (* Harvey P. Dale, Mar 21 2018 *)

CROSSREFS

Sequence in context: A137213 A027853 A132894 * A192431 A329253 A161125

Adjacent sequences:  A117914 A117915 A117916 * A117918 A117919 A117920

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Apr 02 2006

EXTENSIONS

More terms from R. J. Mathar, Mar 17 2008

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 January 24 10:42 EST 2020. Contains 331193 sequences. (Running on oeis4.)