login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A242026 Number of non-palindromic n-tuples of 4 distinct elements. 3
0, 12, 48, 240, 960, 4032, 16128, 65280, 261120, 1047552, 4190208, 16773120, 67092480, 268419072, 1073676288, 4294901760, 17179607040, 68719214592, 274876858368, 1099510579200, 4398042316800, 17592181850112, 70368727400448, 281474959933440, 1125899839733760 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Non-palindromic vs palindromic (DNA) sequences (e.g., {a,c,a,c} is a non-palindromic sequence but {a,c,c,a} is palindromic). Useful in bioinformatics.
LINKS
FORMULA
a(n) = 2^(n-1) * (2^(n+1) + (-1)^n - 3).
a(n) = 4^n - 4^ceiling(n/2) = A000302(n) - A056450(n).
From Colin Barker, Aug 12 2014: (Start)
a(n) = 4*a(n-1) + 4*a(n-2) - 16*a(n-3).
G.f.: 12*x^2 / ((2*x-1)*(2*x+1)*(4*x-1)). (End)
EXAMPLE
For n=2 the a(2)=12 solutions (non-palindromic 2-tuples over 4 distinct elements {a,c,g,t}) are: {a,c}, {a,g}, {a,t}, {c,a}, {c,g}, {c,f}, {g,a},{g,c}, {g,t}, {t,a}, {t,c}, {t,g}.
MATHEMATICA
Table[2^(n-1) * (2^(n+1) + (-1)^n - 3), {n, 66}]
LinearRecurrence[{4, 4, -16}, {0, 12, 48}, 30] (* Harvey P. Dale, May 24 2023 *)
PROG
(PARI) a(n) = ((-1)^n - 3)*2^(n-1) + 4^n; \\ Michel Marcus, Aug 12 2014
(PARI) concat(0, Vec(12*x^2 / ((2*x-1)*(2*x+1)*(4*x-1)) + O(x^100))) \\ Colin Barker, Aug 12 2014
CROSSREFS
Sequence in context: A061148 A339760 A221908 * A340727 A052601 A003498
KEYWORD
nonn,easy
AUTHOR
Mikk Heidemaa, Aug 12 2014
EXTENSIONS
Typos in formula fixed by Colin Barker, Aug 12 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)