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A073970 Number of strings of length n over Z_5 with trace 1 and subtrace 4. 7
0, 1, 6, 30, 125, 600, 3025, 15500, 78000, 390625, 1952500, 9765625, 48831250, 244156250, 1220703125, 6103437500, 30517265625, 152587500000, 762939062500, 3814697265625, 19073484375000, 95367431640625, 476837167968750, 2384185839843750, 11920928955078125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Same as the number of strings of length n over Z_5 with: trace 2 and subtrace 1, trace 3 and subtrace 1, or trace 4 and subtrace 4.

Same as the number of strings of length n over GF(5) with: trace 1 and subtrace 4, trace 2 and subtrace 1, trace 3 and subtrace 1, or trace 4 and subtrace 4.

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^2*(25*x^5 -50*x^4 +15*x^3 -5*x^2 +4*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

EXAMPLE

a(2;3,2)=2 since the two 5-ary strings of trace 3, subtrace 2 and length 2 are { 12, 21 }.

CROSSREFS

Cf. A073963, A073964, A073965, A073966, A073967, A073968, A073969.

Sequence in context: A215225 A056385 A266945 * A074009 A248328 A344344

Adjacent sequences:  A073967 A073968 A073969 * A073971 A073972 A073973

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

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Last modified August 18 12:46 EDT 2022. Contains 356212 sequences. (Running on oeis4.)