OFFSET
1,1
COMMENTS
a(1)=3; then add 0 to the first number, then 1,2,3,4,... and so on.
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = a(n-1) + n - 2 (with a(1)=3). - Vincenzo Librandi, Nov 27 2010
G.f.: x*(3-6*x+4*x^2)/(1-x)^3. - Nikita Gogin, Jul 24 2013
a(n) = A016028(n+1) for n >= 2. - Georg Fischer, Oct 28 2018
Sum_{n>=1} 1/a(n) = 1/3 + 2*Pi*tanh(sqrt(23)*Pi/2)/sqrt(23). - Amiram Eldar, Dec 13 2022
MAPLE
seq(coeff(series(x*(4*x^2-6*x+3)/(1-x)^3, x, n+1), x, n), n = 1 .. 55); # Muniru A Asiru, Oct 28 2018
MATHEMATICA
s=3; lst={3}; Do[s+=n; AppendTo[lst, s], {n, 0, 5!}]; lst
Table[Binomial[n-1, 2], {n, 60}]+3 (* Harvey P. Dale, Feb 27 2013 *)
PROG
(Sage) [3+binomial(n, 2) for n in range(0, 54)] # Zerinvary Lajos, Mar 12 2009
(PARI) Vec( x*(3-6*x+4*x^2)/(1-x)^3 + O(x^66) ) \\ Joerg Arndt, Jul 24 2013
(GAP) List([1..55], n->3+Binomial(n-1, 2)); # Muniru A Asiru, Oct 28 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Dec 15 2008
STATUS
approved