A140430 Period 6: repeat [3, 2, 4, 1, 2, 0].

3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 0, 3, 2

Offset

0,1

Comments

Associate to sequence identical to half its p-th differences.

Corresponding n-th differences table:

3, 2, 4, 1, 2, 0, 3;

-1, 2, -3, 1, -2, 3, -1;

3, -5, 4, -3, 5, -4, 3;

-8, 9, -7, 8, -9, 7, -8;

17, -16, 15, -17, 16, -15, 17;

-33, 31, -32, 33, -31, 32, -33;

64, -63, 65, -64, 63, -65, 64;

Note that the main diagonal is 3 followed by A000079(n+1).

Note also the southeast diagonal 4, 1, 5, 7, 17 is 4 followed by A014551(n+1).

Note also 3*A001045(n+1), one signed and one unsigned, in two southeast diagonals.

Starting from second line, the first column is A130750 signed.

Starting from second line, the second column is A130752 signed.

Starting from second line, the third column is A130755 signed.

Links

Table of n, a(n) for n=0..85.

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

Formula

From Wesley Ivan Hurt, Aug 29 2014: (Start)

G.f.: (3-x+2*x^2)/((1-x)*(1+x^3)).

a(n) = a(n-1)-a(n-3)+a(n-4);

a(n) = 2 + ((-n-2) mod 3) * (-1)^n. (End)

a(n) = (6 + 3*cos(n*Pi) + 2*sqrt(3)*sin(n*Pi/3))/3. - Wesley Ivan Hurt, Jun 20 2016

Maple

A140430:=n->2+((-n-2) mod 3)*(-1)^n: seq(A140430(n), n=0..100); # Wesley Ivan Hurt, Aug 29 2014

Mathematica

CoefficientList[Series[(3 - x + 2 x^2)/((1 - x)*(1 + x^3)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 29 2014 *)
PadRight[{}, 120, {3, 2, 4, 1, 2, 0}] (* Harvey P. Dale, Jan 21 2023 *)

Prog

(PARI) a(n)=[3, 2, 4, 1, 2, 0][n%6+1] \\ Charles R Greathouse IV, Jun 02 2011
(Magma) [2 + ((-n-2) mod 3)*(-1)^n : n in [0..100]]; // Wesley Ivan Hurt, Aug 29 2014

Crossrefs

Cf. A000079 (2^n), A001045 (Jacobsthal), A014551 (Jacobsthal-Lucas).

Cf. A130750, A130752, A130755.

Sequence in context: A154879 A097673 A226377 * A123359 A121885 A187760

Adjacent sequences: A140427 A140428 A140429 * A140431 A140432 A140433

Keyword

nonn,easy

Author

Paul Curtz, Jun 25 2008

Extensions

More terms from Wesley Ivan Hurt, Aug 29 2014

Status

approved