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A073967
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Number of strings of length n over Z_5 with trace 1 and subtrace 1.
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7
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0, 0, 6, 25, 125, 600, 3150, 15750, 78625, 390625, 1952500, 9762500, 48831250, 244140625, 1220703125, 6103437500, 30517656250, 152588281250, 762941015625, 3814697265625, 19073484375000, 95367421875000, 476837167968750, 2384185791015625, 11920928955078125
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listen;
history;
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OFFSET
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1,3
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COMMENTS
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Same as the number of strings of length n over Z_5 with: trace 2 and subtrace 4, trace 3 and subtrace 4, or trace 4 and subtrace 1.
Same as the number of strings of length n over GF(5) with: trace 1 and subtrace 1, trace 2 and subtrace 4, trace 3 and subtrace 4, or trace 4 and subtrace 1.
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LINKS
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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
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FORMULA
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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+75*x^3-85*x^2+35*x-6) / ((5*x-1)*(5*x^2-1)*(25*x^4-25*x^3+15*x^2-5*x+1)). - Colin Barker, Nov 26 2014
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CROSSREFS
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Cf. A073963, A073964, A073965, A073966, A073968, A073969, A073970.
Sequence in context: A215763 A153481 A099359 * A188207 A275541 A082430
Adjacent sequences: A073964 A073965 A073966 * A073968 A073969 A073970
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KEYWORD
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easy,nonn
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AUTHOR
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Frank Ruskey and Nate Kube, Aug 15 2002
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EXTENSIONS
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Terms a(11) onward from Max Alekseyev, Apr 09 2013
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STATUS
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approved
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