OFFSET
1,1
COMMENTS
a(1)=3; then add 1 to the first number, then 2,3,4... and so on.
Numbers m such that 8m-23 is a square. - Bruce J. Nicholson, Jul 25 2017
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Ângela Mestre and José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 3+C(n,2), n>=1. - Zerinvary Lajos, Mar 12 2009
a(n) = a(n-1)+n-1 (with a(1)=3). - Vincenzo Librandi, Nov 27 2010
Sum_{n>=1} 1/a(n) = 2*Pi*tanh(sqrt(23)*Pi/2)/sqrt(23). - Amiram Eldar, Dec 13 2022
MAPLE
MATHEMATICA
s=3; lst={3}; Do[s+=n; AppendTo[lst, s], {n, 1, 5!}]; lst
Table[3 + n*(n-1)/2, {n, 100}] (* Wesley Ivan Hurt, Jan 28 2014 *)
PROG
(Sage) [3+binomial(n, 2) for n in range(1, 55)] # Zerinvary Lajos, Mar 12 2009
(PARI) a(n)=3+n*(n-1)/2 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [3+n*(n-1)/2 : n in [1..50]]; // Wesley Ivan Hurt, Mar 25 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Dec 15 2008
STATUS
approved