OFFSET
0,4
COMMENTS
Binomial transform of A084152.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-3,-10).
FORMULA
a(n) = (5^n - 2*2^n + (-1)^n)/18.
G.f.: x^2/((1+x)*(1-2*x)*(1-5*x)).
E.g.f.: exp(x)*(exp(2*x) - exp(-x))^2/18 = (exp(5*x) - 2*exp(2*x) + exp(-x))/18.
MATHEMATICA
LinearRecurrence[{6, -3, -10}, {0, 0, 1}, 41] (* G. C. Greubel, Oct 10 2022 *)
PROG
(Magma) [(5^n -2^(n+1) +(-1)^n)/18: n in [0..40]]; // G. C. Greubel, Oct 10 2022
(SageMath) [(5^n -2^(n+1) +(-1)^n)/18 for n in range(41)] # G. C. Greubel, Oct 10 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 16 2003
STATUS
approved