OFFSET
0,2
COMMENTS
a(n) also can be represented as n concentric triangles (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) = a(n-1) + 18*n - 15 with n>0, a(0)=0. - Vincenzo Librandi, Nov 26 2010
G.f.: 3*x*(1+5*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011
EXAMPLE
From Omar E. Pol, Aug 21 2011: (Start)
Illustration of initial terms as concentric triangles:
.
. 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
.
. 3 24 63
(End)
MATHEMATICA
s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 3, 6!, 18}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)
3*PolygonalNumber[8, Range[0, 40]] (* Harvey P. Dale, May 08 2022 *)
PROG
(PARI) a(n)=3*n*(3*n-2) \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
Omar E. Pol, Dec 12 2008
STATUS
approved