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

Author

Paul Barry, May 16 2003

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A084152.

Programs

Magma

[(5^n -2^(n+1) +(-1)^n)/18: n in [0..40]]; // G. C. Greubel, Oct 10 2022

Mathematica

LinearRecurrence[{6,-3,-10}, {0,0,1}, 41] (* 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

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.