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!)
A073969 Number of strings of length n over Z_5 with trace 1 and subtrace 3. 7
0, 2, 6, 30, 125, 650, 3150, 15750, 78000, 390625, 1952500, 9768750, 48831250, 244156250, 1220703125, 6103593750, 30517656250, 152588281250, 762939062500, 3814697265625, 19073484375000, 95367441406250, 476837167968750, 2384185839843750, 11920928955078125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Same as the number of strings of length n over Z_5 with: trace 2 and subtrace 2, trace 3 and subtrace 2, or trace 4 and subtrace 3.

Same as the number of strings of length n over GF(5) with: trace 1 and subtrace 3, trace 2 and subtrace 2, trace 3 and subtrace 2, or trace 4 and subtrace 3.

LINKS

Table of n, a(n) for n=1..25.

Max Alekseyev, PARI/GP scripts for miscellaneous math problems

F. Ruskey, Strings over Z_5 with given trace and subtrace

F. Ruskey, Strings over GF(5) with given trace and subtrace

FORMULA

a(n; t, s) = a(n-1; t, s) + a(n-1; t+4, s+4t+1) + a(n-1; t+3, s+3t+4) + a(n-1; t+2, s+2t+4) + a(n-1; t+1, s+t+1).

Empirical g.f.: -x^2*(25*x^5-50*x^4+65*x^3-40*x^2+14*x-2) / ((5*x-1)*(5*x^2-1)*(25*x^4-25*x^3+15*x^2-5*x+1)). - Colin Barker, Nov 26 2014

EXAMPLE

a(2;3,2)=2 since the two 5-ary strings of trace 3, subtrace 2 and length 2 are { 12, 21 }.

CROSSREFS

Cf. A073963, A073964, A073965, A073966, A073967, A073968, A073970.

Sequence in context: A036752 A065563 A035105 * A295863 A224530 A120950

Adjacent sequences:  A073966 A073967 A073968 * A073970 A073971 A073972

KEYWORD

easy,nonn

AUTHOR

Frank Ruskey and Nate Kube, Aug 15 2002

EXTENSIONS

Terms a(11) onward from Max Alekseyev, Apr 09 2013

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 May 17 19:21 EDT 2022. Contains 353778 sequences. (Running on oeis4.)