A272727 a(0)=0; thereafter a(n+1) is the number of coincidences between the sequence so far (a(0), ..., a(n)) and its reverse (a(n), ..., a(0)).

0, 1, 0, 3, 0, 3, 0, 5, 0, 7, 0, 7, 0, 7, 0, 9, 0, 9, 0, 11, 0, 13, 0, 15, 0, 15, 0, 15, 0, 15, 0, 17, 0, 19, 0, 19, 0, 19, 0, 21, 0, 21, 0, 23, 0, 23, 0, 25, 0, 27, 0, 29, 0, 31, 0, 31, 0, 31, 0, 31, 0, 31, 0, 33, 0, 33, 0, 35, 0, 37, 0, 39, 0, 39, 0, 39, 0, 39, 0, 41, 0, 43

Offset

0,4

Comments

a(2n-1) is positive and odd.

a(2n+1) - a(2n-1) is always either 0 or 2.

The number of repetitions of the value 2n-1 is A272729(n).

Links

Ivan Neretin, Table of n, a(n) for n = 0..8191

Formula

a(2n)=0.

a(2n-1)=A272728(n)+n.

Example

A one-element series [0] coincides with its own reverse, hence a(1)=1.
[0,1] and [1,0] differ in every term, hence a(2)=0.
[0,1,0] is its own reverse, hence a(3)=3.
[0,1,0,3] and [3,0,1,0] differ in every term, hence a(4)=0.
[0,1,0,3,0] and [0,3,0,1,0] coincide in three terms, hence a(5)=3.

Mathematica

Nest[Append[#, Count[# - Reverse[#], x_ /; x == 0]] &, {0}, 81]

Crossrefs

Cf. A272728, A272729.

Sequence in context: A292130 A291971 A240923 * A333791 A323135 A356205

Adjacent sequences: A272724 A272725 A272726 * A272728 A272729 A272730

Keyword

nonn

Author

Ivan Neretin, May 05 2016

Status

approved