OFFSET
0,2
COMMENTS
3*A172078(n) = n*a(n) - Sum_{k=0..n-1} a(k). - Bruno Berselli, Dec 12 2010
REFERENCES
"Supplemento al Periodico di Matematica", Raffaello Giusti Editore (Livorno), Jan. 1910 p. 47 (Problem 1052).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 12*n^2 - 9*n = 3*A001107(n).
a(n) = a(n-1)+24*n-21, n>0. - Vincenzo Librandi, Nov 26 2010
a(n) = sum(A001539(k), k=0..n-1)-sum(4*A002939(k), k=0..n-1) if n>0 (see References, Problem 1052). - Bruno Berselli, Dec 08 2010 - Jan 21 2011
G.f.: -3*x*(1+7*x)/(x-1)^3.
a(0)=0, a(1)=3, a(2)=30, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, May 26 2012
EXAMPLE
For n=8, a(8)=(1*3+5*7+9*11+..+29*31)-(2*4+6*8+10*12+..+26*28) = 696 (see Problem 1052 in References). - Bruno Berselli, Dec 12 2010
MATHEMATICA
s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 3, 6!, 24}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 )
Table[3n(4n-3), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 3, 30}, 40] (* Harvey P. Dale, May 26 2012 *)
PROG
(PARI) a(n)=3*n*(4*n-3) \\ Charles R Greathouse IV, Sep 28 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Dec 15 2008
STATUS
approved