A328284 An extension of the Jacobsthal numbers: 0, 0, 1, followed by A001045.

0, 0, 1, 0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, 699051, 1398101, 2796203, 5592405, 11184811, 22369621, 44739243, 89478485

Offset

0,7

Links

Table of n, a(n) for n=0..31.

OEIS Wiki, Autosequence

Index entries for linear recurrences with constant coefficients, signature (1,2).

Formula

a(n) is the fourth row of the following array:

0, 0, 0, 0, 0, 1, 3, 7, 14, 27, 51, 97, ...

0, 0, 0, 0, 1, 2, 4, 7, 13, 24, 46, 89, ... = A086445

0, 0, 0, 1, 1, 2, 3, 6, 11, 22, 43, 86, ... = 0, 0, 0, A005578(n)

0, 0, 1, 0, 1, 1, 3, 5, 11, 21, 43, 85, ... = a(n)

0, 1, -1, 1, 0, 2, 2, 6, 10, 22, 42, 86, ...

1, -2, 2, -1, 2, 0, 4, 4, 12, 20, 44, 84, ...

From the main diagonal onward, every row is an autosequence of the first kind.

From Stefano Spezia, Oct 16 2019: (Start)

O.g.f.: x^2*(-1 + x + x^2)/(-1 + x + 2*x^2).

E.g.f.: (1/24)*exp(-x)*(8 - 9*exp(x) + exp(3*x) + 6*exp(x)*x + 6*exp(x)*x^2).

a(n) = a(n-1) + 2*a(n-2) for n > 4. (End)

a(n) = Sum_{k=0..n-1} A183190(n-k-2, n-2*k-2). - Jean-François Alcover, Nov 10 2019

Mathematica

a[n_] := If[n>3, (2^(n-3) + (-1)^n)/3, If[n == 2, 1, 0]]; (* Jean-François Alcover, Oct 16 2019 *)

Crossrefs

Cf. A000129, A001045, A054977, A139756, A141413, A166444, A183190.

Cf. A000079, A005578, A063524, A086445, A139818, A257113.

Sequence in context: A283702 A284539 A154917 * A167167 A077925 A001045

Adjacent sequences: A328281 A328282 A328283 * A328285 A328286 A328287

Keyword

nonn

Author

Paul Curtz, Oct 11 2019

Extensions

Partially edited by Peter Luschny, Nov 12 2019

Status

approved