OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-1)
FORMULA
a(n) = Sum (L(2i+e), (i=0, 1, .., Floor(n/2))), where L(n) are Lucas numbers and e=2(n/2 - Floor(n/2)).
Convolution of L(n) with the sequence (1, 0, 1, 0, 1, 0, ...)
a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n>3.
G.f.: ( 2-x ) / ( (x-1)*(1+x)*(x^2+x-1) ).
a(n) = 2^(-1-n) * (3*(-2)^n - 2^n + (1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n)). - Colin Barker, Jul 12 2017
MATHEMATICA
CoefficientList[Series[(2-x)/(1-x-2*x^2+x^3+x^4), {x, 0, 40}], x]
PROG
(PARI) Vec((2-x) / ((x-1)*(1+x)*(x^2+x-1)) + O(x^50)) \\ Colin Barker, Jul 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Aug 22 2002
STATUS
approved