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A068774
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Number of strings over Z_4 of length n with trace 0 and subtrace 2.
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11
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0, 0, 0, 8, 40, 240, 1120, 4480, 17280, 65280, 253440, 1015808, 4126720, 16773120, 67624960, 270499840, 1077903360, 4294901760, 17146183680, 68585259008, 274608947200, 1099510579200, 4400191897600, 17600767590400, 70385915658240, 281474959933440
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OFFSET
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1,4
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COMMENTS
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a(n; 0,2) where a(n; t,s) is the number of length n 4-ary strings whose digits sum to t mod 4 and whose sum of products of all pairs of digits sum to s mod 4.
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LINKS
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FORMULA
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a(n; t, s) = a(n-1; t, s) + a(n-1; t+3, s+3t+1) + a(n-1; t+2, s+2t) + a(n-1; t+1, s+t+1) where t is the trace and s is the subtrace.
Empirical g.f.: 8*x^4*(40*x^4-40*x^3+20*x^2-5*x+1) / ((2*x-1)*(4*x-1)*(8*x^2-4*x+1)*(16*x^4+1)). - Colin Barker, Dec 06 2014
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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