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A328284 An extension of the Jacobsthal numbers: 0, 0, 1, followed by A001045. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A001045 A077925

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

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Last modified May 18 22:57 EDT 2021. Contains 344007 sequences. (Running on oeis4.)