A073965 Number of strings of length n over Z_5 with trace 0 and subtrace 2.

0, 0, 6, 30, 150, 650, 3150, 15500, 78000, 390000, 1952500, 9762500, 48831250, 244156250, 1220781250, 6103593750, 30517656250, 152587500000, 762939062500, 3814695312500, 19073484375000, 95367421875000, 476837167968750, 2384185839843750, 11920929199218750

Offset

1,3

Comments

Same as the number of strings of length n over Z_5 with trace 0 and subtrace 3.

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

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

Same as the number of strings of length n over GF(5) with trace 1 and subtrace 0.

Same as the number of strings of length n over GF(5) with trace 4 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.: 2*x^3*(50*x^4-50*x^3+30*x^2-15*x+3) / ((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. A073963, A073964, A073966, A073967, A073968, A073969, A073970.

Sequence in context: A319377 A079738 A127741 * A214940 A002913 A157519

Adjacent sequences: A073962 A073963 A073964 * A073966 A073967 A073968

Keyword

easy,nonn

Author

Frank Ruskey, Nate Kube, Aug 15 2002

Extensions

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

Status

approved