OFFSET
0,1
COMMENTS
First differences of A002943. - Aaron David Fairbanks, May 13 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 07 2011
A089911(3*a(n)) = 4. - Reinhard Zumkeller, Jul 05 2013
From Michael Somos, May 15 2014: (Start)
G.f.: (6 + 2*x) / (1 - x)^2.
E.g.f.: (6 + 8*x) * exp(x). (End)
Sum_{n>=0} (-1)^n/a(n) = (Pi + log(3-2*sqrt(2)))/(8*sqrt(2)). - Amiram Eldar, Dec 11 2021
EXAMPLE
G.f. = 6 + 14*x + 22*x^2 + 30*x^3 + 38*x^4 + 46*x^5 + 54*x^6 + 62*x^7 + ...
MAPLE
MATHEMATICA
Range[6, 1000, 8] (* Vladimir Joseph Stephan Orlovsky, May 27 2011 *)
8Range[0, 60]+6 (* or *) LinearRecurrence[{2, -1}, {6, 14}, 60] (* Harvey P. Dale, Nov 14 2021 *)
PROG
(Magma) [8*n+6: n in [0..60]]; // Vincenzo Librandi, Jun 07 2011
(Haskell)
a017137 = (+ 6) . (* 8) -- Reinhard Zumkeller, Jul 05 2013
(PARI) a(n) = 8*n+6; \\ Michel Marcus, Sep 17 2015
(PARI) Vec((6+2*x)/(1-x)^2 + O(x^100)) \\ Altug Alkan, Oct 23 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 11 1996
STATUS
approved