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

1,2

Links

Table of n, a(n) for n=1..28.

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]

Example

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}.

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}]

Prog

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

Crossrefs

Cf. A167993, A233411, A242026, A240437.

Sequence in context: A129369 A095853 A027266 * A129796 A129790 A121156

Adjacent sequences: A242275 A242276 A242277 * A242279 A242280 A242281

Keyword

nonn,easy

Author

Mikk Heidemaa, Aug 16 2014

Status

approved