A092434 Number of words X=x(1)x(2)x(3)...x(n) of length n in three digits {0,1,2} that are invariant under the mapping X -> Y, where y(i)=((AD)^(i-1))x(1) and where (AD) denotes the absolute difference (AD)x(i)=abs(x(i+1)-x(i)) (in other words, y(i) is the i-th element in the diagonal of leading entries in the table of absolute differences of {x(1), x(2),...,x(n)}).

3, 4, 10, 12, 28, 32, 72, 80, 176, 192, 416, 448, 960, 1024

Offset

1,1

Comments

In the two digits {0,1} the corresponding sequence is 2,2,4,4,8,8,16,16,32,32,64,64,... which appears to be A060546.

Links

Table of n, a(n) for n=1..14.

Formula

It is conjectured that a(n)=(n+2)*2^((n-1) div 2).

Example

The table of absolute differences of {2,1,1,0} is
2
1.1
1.0.1
0.1.1.0
with the diagonal of leading absolute differences again forming the word (2110).
Thus (2110) is one of the twelve words in the digits {0,1,2} that are counted in calculating a(4).

Crossrefs

Cf. A060546.

Sequence in context: A101506 A362553 A360620 * A239632 A031367 A379494

Adjacent sequences: A092431 A092432 A092433 * A092435 A092436 A092437

Keyword

nonn,more

Author

John W. Layman, Mar 23 2004

Status

approved