OFFSET
1,1
COMMENTS
Numbers m >= 9 such that 8*m - 47 is a square. - Bruce J. Nicholson, Jul 25 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = a(n-1) + n = 3*a(n-1) - 3*a(n-2) + a(n-3) = A145018(n+2) + 2.
G.f.: -x*(9 - 15*x + 7*x^2)/(x-1)^3.
E.g.f.: (1/2)*(14 + 4*x + x^2)*exp(x) - 7. - G. C. Greubel, Apr 26 2016
Sum_{n>=1} 1/a(n) = -13/42 + 2*Pi*tanh(sqrt(47)*Pi/2)/sqrt(47). - Amiram Eldar, Dec 13 2022
MATHEMATICA
Table[n*(n+3)/2+7, {n, 1, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {9, 12, 16}, 40] (* Vincenzo Librandi, Mar 15 2012 *)
PROG
(Magma) I:=[9, 12, 16]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Mar 15 2012
(PARI) for(n=1, 40, print1(n*(n+3)/2+7, ", ")); \\ Vincenzo Librandi, Mar 15 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Oct 08 2009
EXTENSIONS
Definition replaced by polynomial from R. J. Mathar, Oct 12 2009
STATUS
approved