A096269 a(n) = number of distinct palindromes of length n that occur in A096268.

2, 1, 3, 0, 4, 0, 3, 0, 4, 0, 4, 0, 3, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 3, 0, 3, 0, 3, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

J.-P. Allouche, M. Baake, J. Cassaigns, and D. Damanik, Palindrome complexity, arXiv:math/0106121 [math.CO], 2001; Theoretical Computer Science, 292 (2003), 9-31.

D. Damanik, Local symmetries in the period-doubling sequence, Discrete Appl. Math., 100 (2000), 115-121.

Formula

For even n >= 4, a(n) = 0; for odd n >= 5, a(n) = a(2n-1) = a(2n+1).

For odd n >= 5, let x be the power of 2 closest to n; if n > x then a(n) = 4 and if n < x then a(n) = 3. - David Wasserman, Nov 01 2007

Prog

(PARI) A096269(n) = if(n<=2, 3-n, if(3==n, n, if(!(n%2), 0, my(pp2=2^(#binary(n)-1)); if(((2*pp2)-n)<(n-pp2), 3, 4)))); \\ Antti Karttunen, Mar 30 2021

Crossrefs

Cf. A096268.

Sequence in context: A092093 A197386 A357991 * A260437 A262677 A307742

Adjacent sequences: A096266 A096267 A096268 * A096270 A096271 A096272

Keyword

nonn,easy,base

Author

N. J. A. Sloane, Jun 22 2004

Extensions

More terms from David Wasserman, Nov 01 2007

Status

approved