A084153 Binomial transform of a Jacobsthal convolution.

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.

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

Cf. A084152.

Sequence in context: A282371 A291004 A203155 * A086314 A086091 A081893

Adjacent sequences: A084150 A084151 A084152 * A084154 A084155 A084156

Keyword

easy,nonn

Author

Paul Barry, May 16 2003

Status

approved