OFFSET
0,1
COMMENTS
2*a(i) + 3 is prime for i = 0..14. - Vincenzo Librandi, Jun 01 2014
Numbers m >= 8 such that 8*m - 55 is a square. - Bruce J. Nicholson, Jul 26 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = n + a(n-1) + 1 with n > 1, a(1)=10.
G.f.: (8 - 14*x + 7*x^2)/(1 - x)^3. - Vincenzo Librandi, Sep 16 2013
a(n) = Sum_{i=n-5..n+7} i*(i+1)/26. - Bruno Berselli, Oct 20 2016
Sum_{n>=0} 1/a(n) = -1/7 + 2*Pi*tanh(sqrt(55)*Pi/2)/sqrt(55). - Amiram Eldar, Dec 13 2022
From Elmo R. Oliveira, Oct 31 2024: (Start)
E.g.f.: exp(x)*(8 + 2*x + x^2/2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
MATHEMATICA
Table[n (n + 3)/2 + 8, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 03 2011 *)
CoefficientList[Series[(8 - 14 x + 7 x^2) / (1 - x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Sep 16 2013 *)
LinearRecurrence[{3, -3, 1}, {8, 10, 13}, 60] (* Harvey P. Dale, Jul 05 2020 *)
PROG
(Magma) [n*(n+3)/2+8: n in [0..60]]; // Vincenzo Librandi, Sep 16 2013
(PARI) a(n)=n*(n+3)/2+8 \\ Charles R Greathouse IV, Jun 16 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 07 2009
STATUS
approved