OFFSET
0,2
COMMENTS
a(n) can be represented as a figurate number using n concentric pentagons (see example). - Omar E. Pol, Aug 21 2011
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 5*A000326(n).
a(n) = a(n-1)+15*n-10 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010
E.g.f.: (5/2)*(3*x^2 + 2*x)*exp(x). - G. C. Greubel, Jul 17 2017
From Amiram Eldar, Feb 26 2022: (Start)
Sum_{n>=1} 1/a(n) = (9*log(3) - sqrt(3)*Pi)/15.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*(sqrt(3)*Pi- 6*log(2))/15. (End)
EXAMPLE
From Omar E. Pol, Aug 22 2011 (Start):
Illustration of initial terms as concentric pentagons (in a precise representation the pentagons should be strictly concentric):
.
. o
. o o
. o o
. o o o o
. o o o o o o
. o o o o o o
. o o o o o o o o o
.o o o o o o o o o o o o
. o o o o o o o o o o o o
. o o o o o o
. o o o o o o
. o o o o o o o o o o o o
. o o
. o o
. o o o o o o o o
.
. 5 25 60
(End)
MAPLE
MATHEMATICA
Table[5 n (3 n - 1)/2, {n, 0, 50}] (* Wesley Ivan Hurt, Sep 19 2014 *)
5*PolygonalNumber[5, Range[0, 50]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 13 2020 *)
PROG
(Magma) [5*n*(3*n-1)/2 : n in [0..50]]; // Wesley Ivan Hurt, Sep 19 2014
(PARI) a(n)=5*n*(3*n-1)/2 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Dec 11 2008
STATUS
approved