OFFSET
1,1
COMMENTS
LINKS
Wikipedia, Cube (algebra)
Index entries for linear recurrences with constant coefficients, signature (0,2).
FORMULA
a(n) = ceiling((9 - (- 1)^n)*2^(floor(n/2) - 2)).
a(n) = n + 2 for n <= 3; a(n) = 2*a(n-2) for n > 3.
From Bruno Berselli, Aug 20 2013: (Start)
G.f.: x*(3+4*x-x^2)/(1-2*x^2).
a(n) = (16-(8-5*r)*(1-(-1)^n))*r^(n-6) for n>1, r=sqrt(2). (End)
EXAMPLE
a(9) = 40 because it is equal to 5*2^(4-1).
MATHEMATICA
CoefficientList[Series[(3 + 4 x - x^2)/(1 - 2 x^2), {x, 0, 50}], x] (* Bruno Berselli, Aug 20 2013 *)
PROG
(Magma) [n le 3 select n+2 else 2*Self(n-2) : n in [1..43]]
(PARI) r=43; print1(3); print1(", "); for(n=2, r, if(bitand(n, 1), print1(5*2^((n-3)/2)), print1(2^(n/2+1))); print1(", "));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Arkadiusz Wesolowski, Aug 20 2013
STATUS
approved