OFFSET
1,2
REFERENCES
T. M. Apostol, Calculus, Volume 1, John Wiley & Sons, 1967 (2nd ed.), p. 378-379.
LINKS
Bruno Berselli, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
FORMULA
G.f.: x*(1 + 2*x - 2*x^2 + 2*x^3 + x^4)/(1-x^2)^3.
a(n) = a(-n) = 1+((-1)^n+1)*(n^2-2)/4.
MATHEMATICA
CoefficientList[Series[(1 + 2 x - 2 x^2 + 2 x^3 + x^4) / (1 - x^2)^3, {x, 0, 65}], x] (* Vincenzo Librandi, Aug 19 2013 *)
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {1, 2, 1, 8, 1, 18}, 70] (* Harvey P. Dale, Jul 18 2024 *)
PROG
(Magma) &cat[[1, 2*n^2]: n in [1..33]];
(Magma) [1+((-1)^n+1)*(n^2-2)/4: n in [1..70]]; // Vincenzo Librandi, Aug 19 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Jan 11 2011
STATUS
approved