OFFSET
1,1
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
From R. J. Mathar, Nov 22 2009: (Start)
a(n) = a(n-1) +a(n-2) -a(n-3).
a(n) = (9 + 14*n + 7*(-1)^n)/4.
G.f.: x*(4 + 7*x - 4*x^2)/((1+x)* (x-1)^2). (End)
E.g.f.: (1/4)*(7 - 16*exp(x) + (9 + 14*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 15 2016
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {4, 11, 11}, 60] (* Vincenzo Librandi, Feb 28 2012 *)
Join[{4}, With[{c=LinearRecurrence[{2, -1}, {11, 18}, 50]}, Riffle[c, c]]] (* or *) With[{c=7*Range[0, 50]+4}, Rest[Riffle[c, c]]] (* Harvey P. Dale, May 09 2018 *)
PROG
(Magma) I:=[4, 11, 11]; [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