A242278 Number of non-palindromic n-tuples of 3 distinct elements.

0, 6, 18, 72, 216, 702, 2106, 6480, 19440, 58806, 176418, 530712, 1592136, 4780782, 14342346, 43040160, 129120480, 387400806, 1162202418, 3486725352, 10460176056, 31380882462, 94142647386, 282429005040, 847287015120, 2541864234006, 7625592702018, 22876787671992

Offset: 1

Author

Mikk Heidemaa, Aug 16 2014

Keywords

• nonn
• easy

Examples

			For n=3, the a(3)=18 solutions (non-palindromic 3-tuples) are:
{0,0,1}, {0,0,2}, {0,1,1}, {0,1,2}, {0,2,1}, {0,2,2}, {1,0,0}, {1,0,2},
{1,1,0}, {1,1,2}, {1,2,0}, {1,2,2}, {2,0,0}, {2,0,1}, {2,1,0}, {2,1,1},
{2,2,0}, {2,2,1}.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3, 3, -9).

Crossrefs

Cf. A167993, A233411, A242026, A240437.

Programs

Maple

A242278:=n->(1/2)* 3^(n/2) * ((sqrt(3)-1) * (-1)^n - sqrt(3)-1) + 3^n: seq(A242278(n), n=1..28); # Wesley Ivan Hurt, Aug 17 2014.

Mathematica

Table[1/2 * 3^(n/2) * ((Sqrt(3)-1) * (-1)^n - Sqrt(3)-1) + 3^n, {n, 28}]

PARI

a(n)=3^n-3^ceil(n/2) \\ Charles R Greathouse IV, Dec 10 2014

Formula

a(n) = 1/2 * 3^(n/2) * ((sqrt(3)-1)*(-1)^n - sqrt(3)-1) + 3^n.

a(n) = 3^n - 3^ceiling(n/2).

a(n) = A000244(n) - A056449(n).

G.f.: (6*x) / (1 - 3*x - 3*x^2 + 9*x^3).

a(n) = 6*A167993(n). [Bruno Berselli, Aug 19 2014]