OFFSET
0,4
COMMENTS
Inverse binomial transform of phi(phi(3^n)).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,3,2).
FORMULA
a(n)=3a(n-2)+2a(n-3); a(n)=2^(n+1)/9+(7-3n)(-1)^n/9; a(n)=a(n)=sum{k=0..n, (-1)^(n-k)*C(n, k)phi(phi(3^k))}; a(n)=sum{k=0..n, (-1)^(n-k)*C(n, k)(2*3^k/9+C(1, k)/3+4*C(0, k)/9)}; a(n)=sum{k=0..n, J(n-k+1)((-1)^(k+1)-2C(1, k)+4C(0, k))} where J(n)=A001045(n).
MATHEMATICA
CoefficientList[Series[(1-2x^2)/((1-2x)(1+x)^2), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 3, 2}, {1, 0, 1}, 40] (* Harvey P. Dale, Aug 20 2015 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 09 2005
STATUS
approved