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

Author

Paul Curtz, Jun 25 2008

Keywords

• nonn
• easy

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

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

Crossrefs

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

Cf. A130750, A130752, A130755.

Programs

Magma

[2 + ((-n-2) mod 3)*(-1)^n : n in [0..100]]; // Wesley Ivan Hurt, Aug 29 2014

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 *)

PARI

a(n)=[3,2,4,1,2,0][n%6+1] \\ Charles R Greathouse IV, Jun 02 2011

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

Extensions

More terms from Wesley Ivan Hurt, Aug 29 2014