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A073966 Number of strings of length n over Z_5 with trace 1 and subtrace 0. 7
1, 2, 6, 20, 125, 625, 3150, 15500, 78000, 390625, 1955625, 9768750, 48831250, 244125000, 1220703125, 6103515625, 30517656250, 152587500000, 762939062500, 3814697265625, 19073494140625, 95367441406250, 476837167968750, 2384185742187500, 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 0, trace 3 and subtrace 0, or trace 4 and subtrace 0.

Same as the number of strings of length n over GF(5) with: trace 2 and subtrace 0, or trace 3 and subtrace 0.

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*(25*x^6 -50*x^5 +15*x^4 +20*x^3 -21*x^2 +8*x -1) / ((5*x -1)*(5*x^2 -1)*(25*x^4 -25*x^3 +15*x^2 -5*x +1)). - Colin Barker, Nov 25 2014

CROSSREFS

Cf. A073963, A073964, A073965, A073967, A073968, A073969, A073970.

Sequence in context: A136795 A074115 A013206 * A013203 A007847 A274714

Adjacent sequences:  A073963 A073964 A073965 * A073967 A073968 A073969

KEYWORD

easy,nonn

AUTHOR

Frank Ruskey, Nate Kube, Aug 15 2002

EXTENSIONS

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

STATUS

approved

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Last modified August 18 13:09 EDT 2022. Contains 356212 sequences. (Running on oeis4.)