A073963 Number of strings of length n over Z_5 with trace 0 and subtrace 0.

1, 1, 1, 25, 125, 625, 3025, 15625, 78625, 393125, 1955625, 9765625, 48815625, 244140625, 1220703125, 6103515625, 30517265625, 152587890625, 762941015625, 3814705078125, 19073494140625, 95367431640625, 476837119140625, 2384185791015625, 11920928955078125

Offset

1,4

Comments

Same as the number of strings of length n over GF(5) with trace 0 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*(525*x^6-525*x^5+190*x^4-26*x^2+9*x-1) / ((5*x-1)*(5*x^2-1)*(25*x^4-25*x^3+15*x^2-5*x+1)). - Colin Barker, Apr 03 2015

Crossrefs

Cf. A073964, A073965, A073966, A073967, A073968, A073969, A073970.

Sequence in context: A211595 A066609 A074006 * A316277 A201842 A057902

Adjacent sequences: A073960 A073961 A073962 * A073964 A073965 A073966

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