OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = (4*n + 3 + 7*(-1)^n)/2. - Jon E. Schoenfield, Jun 24 2010
G.f.: x^2*(9-5*x)/((1+x)*(1-x)^2). - Vincenzo Librandi, Feb 28 2012
E.g.f.: (1/2)*(7 - 10*exp(x) + (3 + 4*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 15 2016
Sum_{n>=2} (-1)^(n+1)/a(n) = 6/5 - Pi/8 - 3*log(2)/4. - Amiram Eldar, Feb 23 2023
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {0, 9, 4}, 60] (* Vincenzo Librandi, Feb 28 2012 *)
nxt[{n_, a_}]:={n+1, 4n-a+5}; NestList[nxt, {1, 0}, 70][[;; , 2]] (* Harvey P. Dale, Mar 04 2023 *)
PROG
(Magma) I:=[0, 9, 4]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 28 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 20 2009
STATUS
approved