login
A010010
a(0) = 1, a(n) = 20*n^2 + 2 for n>0.
4
1, 22, 82, 182, 322, 502, 722, 982, 1282, 1622, 2002, 2422, 2882, 3382, 3922, 4502, 5122, 5782, 6482, 7222, 8002, 8822, 9682, 10582, 11522, 12502, 13522, 14582, 15682, 16822, 18002, 19222, 20482, 21782, 23122, 24502, 25922, 27382, 28882, 30422, 32002, 33622
OFFSET
0,2
FORMULA
a(n) = A033571(n)+A158186(n) = A158187(n)*2 for n>0. - Reinhard Zumkeller, Mar 13 2009
G.f.: (1+x)*(1+18*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012
E.g.f.: (x*(x+1)*20+2)*e^x-1. - Gopinath A. R., Feb 14 2012
Sum_{n>=0} 1/a(n) = 3/4+sqrt(10)/40*Pi*coth(Pi/sqrt(10)) = 1.0772981051444036327... - R. J. Mathar, May 07 2024
a(n) = A069133(n)+A069133(n+1). - R. J. Mathar, May 07 2024
MATHEMATICA
Join[{1}, 20 Range[41]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {22, 82, 182}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)
PROG
(Magma) [1] cat [20*n^2 + 2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015
CROSSREFS
Cf. A206399.
Sequence in context: A253304 A094844 A323251 * A237618 A105101 A235766
KEYWORD
nonn,easy
AUTHOR
STATUS
approved