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A084153
Binomial transform of a Jacobsthal convolution.
2
0, 0, 1, 6, 33, 170, 861, 4326, 21673, 108450, 542421, 2712446, 13562913, 67815930, 339082381, 1695417366, 8477097753, 42385510610, 211927596741, 1059638071086, 5298190530193, 26490953000490, 132454765701501, 662273829905606
OFFSET
0,4
COMMENTS
Binomial transform of A084152.
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
Cf. A084152.
Sequence in context: A282371 A291004 A203155 * A086314 A086091 A081893
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 16 2003
STATUS
approved