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
a(n) = 6*n - a(n-1) - 4, with n>1, a(1)=4.
From Vincenzo Librandi, Sep 17 2013: (Start)
G.f.: 2*x*(2 + x^2)/((1+x)*(1-x)^2).
a(n) = a(n-1) +a(n-2) -a(n-3). (End)
E.g.f.: (1/2)*(-3 + 4*exp(x) + (6*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 18 2016
MATHEMATICA
With[{c = 6 Range[0, 30] + 4}, Riffle[c, c]] (* or *) RecurrenceTable[ {a[1] == 4, a[n] == 6 n - a[n-1] - 4}, a, {n, 60}] (* Harvey P. Dale, Jun 12 2012 *)
Table[3 n - 3 (-1)^n/2 - 1/2, {n, 70}] (* Bruno Berselli, Sep 17 2013 *)
CoefficientList[Series[(4 + 2 x^2) / ((1 + x) (1 - x)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 17 2013 *)
PROG
(Magma) [n eq 1 select n+3 else 6*n-Self(n-1)-4: n in [1..70]]; // Vincenzo Librandi, Sep 17 2013
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Vincenzo Librandi, Nov 23 2009
EXTENSIONS
New definition by Bruno Berselli, Sep 17 2013
STATUS
approved