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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007613 (8^n + 2(-1)^n )/3.
(Formerly M2129)
9
1, 2, 22, 170, 1366, 10922, 87382, 699050, 5592406, 44739242, 357913942, 2863311530, 22906492246, 183251937962, 1466015503702, 11728124029610, 93824992236886, 750599937895082, 6004799503160662, 48038396025285290, 384307168202282326, 3074457345618258602 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals row sums of triangle A139459(n+1). Example: 170 = (1 + 84 + 84 + 1). Triangle A139459 = the ConvOffsStoT transform of the dodecahedral numbers, A006566. - Gary W. Adamson, Apr 22 2008

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

D. S. Clark, Proof without words, Math. Mag., 63 (1990), 29.

Index entries for linear recurrences with constant coefficients, signature (7,8).

FORMULA

a(n) = A078008(3*n). - Paul Barry, Nov 29 2003

a(n) = (A082311(n)+(-1)^n)/2=(A001045(3*n+1)+(-1)^n)/2. - Paul Barry, Mar 24 2004

a(n) = sum(k=0..n, binomial(3*n, 3*k) ). - Paul Barry, Jan 13 2005

a(n) = 8*a(n-1)+6*(-1)^n. - Paul Curtz, Nov 19 2007

a(n) = 7*a(n-1)+8*a(n-2). G.f.: (5*x-1) / ((x+1)*(8*x-1)). - Colin Barker, Sep 29 2014

PROG

(PARI) a(n)=(8^n + 2(-1)^n )/3 \\ Charles R Greathouse IV, Jun 06, 2011

(MAGMA) [(8^n + 2*(-1)^n )/3: n in [0..20]]; // Vincenzo Librandi, Aug 14 2011

(PARI) Vec((5*x-1)/((x+1)*(8*x-1)) + O(x^100)) \\ Colin Barker, Sep 29 2014

CROSSREFS

Cf. A006566, A139459.

Sequence in context: A230835 A270407 A000184 * A279801 A043037 A058441

Adjacent sequences:  A007610 A007611 A007612 * A007614 A007615 A007616

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

EXTENSIONS

More terms from Colin Barker, Sep 29 2014

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 25 18:49 EST 2018. Contains 299655 sequences. (Running on oeis4.)