OFFSET
0,1
COMMENTS
A139851, which lists primes of the form 4x^2 + 4xy + 29y^2, contains all prime values of a(n). - Altug Alkan, Oct 02 2015
LINKS
FORMULA
a(n) = a(n-1) + A005408(n), a(0) = 29, for n > 0. - Altug Alkan, Oct 02 2015
From Vincenzo Librandi, Oct 03 2015: (Start)
G.f.: (29 - 55*x + 28*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
a(n) = A005563(n) + 29. - Omar E. Pol, Oct 17 2015
E.g.f.: (29 + 3*x + x^2)*exp(x). - Elmo R. Oliveira, Oct 19 2024
EXAMPLE
For n = 3, a(3) = 3^2 + 2*3 + 29 = 44.
MATHEMATICA
Table[n^2 + 2 n + 29, {n, 0, 50}] (* Bruno Berselli, Oct 25 2015 *)
LinearRecurrence[{3, -3, 1}, {29, 32, 37}, 50] (* Harvey P. Dale, Oct 14 2023 *)
PROG
(Python) def a(x):return x*x+2*x+27
(PARI) vector(50, n, n--; n^2+2*n+29) \\ Altug Alkan, Oct 02 2015
(PARI) Vec((29 - 55*x + 28*x^2)/(1-x)^3 + O(x^100)) \\ Altug Alkan, Oct 17 2015
(Magma) [n^2+2*n+29: n in [0..50]]; // Vincenzo Librandi, Oct 03 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jake Saville, Oct 02 2015
STATUS
approved