OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
FORMULA
From R. J. Mathar, Oct 08 2011: (Start)
G.f.: ( x^2*(3-2*x+3*x^2) ) / ( (x^2+1)*(x-1)^2 ).
a(n) = 2*n-2-cos(n*Pi/2). (End)
From Wesley Ivan Hurt, May 22 2016: (Start)
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
a(n) = 2n - 2 - (i^(-n) + i^n)/2 where i = sqrt(-1).
Sum_{n>=2} (-1)^n/a(n) = 3*log(2)/4 + sqrt(2)*log(3-2*sqrt(2))/8. - Amiram Eldar, Dec 21 2021
MAPLE
MATHEMATICA
Table[2n-2-(I^(-n)+I^n)/2, {n, 80}] (* Wesley Ivan Hurt, May 22 2016 *)
LinearRecurrence[{2, -2, 2, -1}, {0, 3, 4, 5}, 80] (* Harvey P. Dale, Mar 27 2023 *)
PROG
(Sage) [lucas_number1(n, 0, 1)+2*n for n in range(0, 55)] # Zerinvary Lajos, Mar 09 2009
(Magma) [n : n in [0..150] | n mod 8 in [0, 3, 4, 5]]; // Wesley Ivan Hurt, May 22 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Wesley Ivan Hurt, May 22 2016
STATUS
approved