A073966 Number of strings of length n over Z_5 with trace 1 and subtrace 0.

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

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