OFFSET
0,4
COMMENTS
Transform of Pell numbers under the mapping g(x)-> (1/(1-x))g(x^2/((1-x)^2).
Binomial transform of aerated Pell numbers 0,0,1,0,2,0,5,0,12,...
LINKS
Andrew Woods, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (4,-4,0,2).
FORMULA
G.f.: x^2*(1-x)/(1 - 4*x + 4*x^2 - 2*x^4).
a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-4).
a(n) = sum_{k=0..n} binomial(n, k) * A000129(k/2) * (1+(-1)^k)/2.
MATHEMATICA
CoefficientList[Series[x^2*(1-x)/(1 - 4*x + 4*x^2 - 2*x^4), {x, 0, 40}], x] (* Vaclav Kotesovec, Jan 05 2015 *)
LinearRecurrence[{4, -4, 0, 2}, {0, 0, 1, 3}, 30] (* Harvey P. Dale, Aug 05 2018 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Dec 22 2004
STATUS
approved