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!)
A073968 Number of strings of length n over Z_5 with trace 1 and subtrace 2. 7
0, 0, 1, 20, 125, 650, 3150, 15625, 78000, 390625, 1952500, 9762500, 48815625, 244125000, 1220703125, 6103593750, 30517656250, 152587890625, 762939062500, 3814697265625, 19073484375000, 95367421875000, 476837119140625, 2384185742187500, 11920928955078125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

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

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^3*(25*x^4-50*x^3+40*x^2-10*x-1) / ((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(3;1,2)=1 since the one 5-ary string of trace 1, subtrace 2 and length 3 is { 222 }.

CROSSREFS

Cf. A073963, A073964, A073965, A073966, A073967, A073969, A073970.

Sequence in context: A249709 A250648 A250421 * A219710 A263229 A125330

Adjacent sequences:  A073965 A073966 A073967 * A073969 A073970 A073971

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 August 18 11:47 EDT 2022. Contains 356212 sequences. (Running on oeis4.)