A084169 A Pell Jacobsthal product.

0, 1, 2, 15, 60, 319, 1470, 7267, 34680, 168435, 810898, 3921103, 18918900, 91381991, 441150502, 2130258075, 10285325040, 49663079099, 239791814010, 1157823924167, 5590452446700, 26993130847215, 130334271942158

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,13,4,-4).

Formula

a(n) = (2^n - (-1)^n)*( (1+sqrt(2))^n - (1-sqrt(2))^n )/(6*sqrt(2)).

a(n) = A001045(n)*A000129(n).

G.f.: x*(1-2*x^2)/((1+2*x-x^2)*(1-4*x-4*x^2)). - Colin Barker, May 01 2012

a(n) = (A007985 + 2*A057087(n))/3. - R. J. Mathar, Sep 29 2020

Mathematica

LinearRecurrence[{2, 13, 4, -4}, {0, 1, 2, 15}, 41] (* G. C. Greubel, Oct 11 2022 *)

Prog

(Magma) [0] cat [(2^n-(-1)^n)*Evaluate(DicksonSecond(n-1, -1), 2)/3: n in [1..40]]; // G. C. Greubel, Oct 11 2022
(SageMath)
def A084169(n): return (2^n-(-1)^n)*lucas_number1(n, 2, -1)/3
[A084169(n) for n in range(41)] # G. C. Greubel, Oct 11 2022

Crossrefs

Cf. A000129, A001045, A007985, A057087.

Sequence in context: A126019 A071237 A006470 * A337905 A296661 A000181

Adjacent sequences: A084166 A084167 A084168 * A084170 A084171 A084172

Keyword

nonn,easy

Author

Paul Barry, May 18 2003

Status

approved