A073968 Number of strings of length n over Z_5 with trace 1 and subtrace 2.

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

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