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) = 8*n - a(n-1) - 6 with n>1, a(1)=5.
a(1) = 5, a(2)=5, a(3)=13; for n>3, a(n) = a(n-1) +a(n-2) -a(n-3). - Harvey P. Dale, Jan 27 2013
G.f.: x*(5 + 3*x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 18 2013
E.g.f.: (-2 + 3*exp(x) + (4*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 19 2016
a(n) = A168379(n) - 2. - Filip Zaludek, Nov 01 2016
MATHEMATICA
RecurrenceTable[{a[1]==5, a[n]==8n-a[n-1]-6}, a, {n, 80}] (* or *) LinearRecurrence[{1, 1, -1}, {5, 5, 13}, 80] (* or *) With[{c= LinearRecurrence[ {2, -1}, {5, 13}, 40]}, Riffle[c, c]] (* Harvey P. Dale, Jan 27 2013 *)
Table[5 + 8 Floor[(n - 1)/2], {n, 60}] (* Bruno Berselli, Sep 18 2013 *)
CoefficientList[Series[(5 + 3 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 18 2013 *)
PROG
(Magma) [5+8*Floor((n-1)/2): n in [1..70]]; // Vincenzo Librandi, Sep 18 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 24 2009
EXTENSIONS
New definition by Vincenzo Librandi, Sep 18 2013
STATUS
approved