OFFSET
1,2
COMMENTS
LINKS
Todd Silvestri, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).
FORMULA
a(n) = 2*n*(n+2)+(-1)^n-4*sin((Pi*n)/2).
G.f.: - x*(x^5-x^4+15*x+1)/((x-1)^3*(x^3+x^2+x+1)).
a(n) = 2*a(n-1) - a(n-2) + 16 if n == 2 mod 4, a(n) = 2*a(n-1) - a(n-2) otherwise. - Robert Israel, Nov 04 2014
a(n) = 2*n*(n+2) - (1-(-1)^n)*(1-2*i^(n+1)) + 1, where i=sqrt(-1). - Bruno Berselli, Nov 18 2014
MAPLE
seq(2*n*(n+2)+(-1)^n-4*sin((Pi*n)/2), n=1..100); # Robert Israel, Nov 04 2014
MATHEMATICA
a[n_Integer/; n>0]:=2 n (n+2)+(-1)^n-4 Mod[n^2 (3 n+2), 4, -1]
CoefficientList[Series[-(x^5 - x^4 + 15 x + 1) / ((x - 1)^3 (x^3 + x^2 + x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 16 2014 *)
Table[2 n (n + 2) - (1 - (-1)^n) (1 - 2 I^(n + 1)) + 1, {n, 1, 50}] (* Bruno Berselli, Nov 18 2014 *)
LinearRecurrence[{2, -1, 0, 1, -2, 1}, {1, 17, 33, 49, 65, 97}, 50] (* Harvey P. Dale, Sep 29 2019 *)
PROG
(PARI) a(n) = 2*n*(n+2)+(-1)^n-4*round(sin((Pi*n)/2)) \\ Charles R Greathouse IV, Nov 17 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Todd Silvestri, Oct 27 2014
STATUS
approved