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A082160
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Deterministic completely defined acyclic automata with 3 inputs and n+1 transient labeled states including a unique state having all transitions to the absorbing state.
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6
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1, 7, 315, 45682, 15646589, 10567689552, 12503979423607, 23841011541867520, 68835375121428936153, 286850872894190847235840, 1660638682341609286358474579, 12947089879912710544534553836032
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OFFSET
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0,2
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COMMENTS
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This is the first column of the array A082172.
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LINKS
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FORMULA
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a(n) = b_3(n) where b_3(0) = 1, b_3(n) = Sum_{i=0..n-1} binomial(n, i)*(-1)^(n-i-1)*((i+2)^3 - 1)^(n-i)*b_3(i), n > 0.
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MATHEMATICA
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a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, i] (-1)^(n - i - 1) ((i + 2)^3 - 1)^(n - i) a[i], {i, 0, n - 1}];
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PROG
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(Magma)
if n eq 0 then return 1;
else return (&+[Binomial(n, j)*(-1)^(n-j-1)*((j+2)^3 - 1)^(n-j)*a(j): j in [0..n-1]]);
end if;
end function;
(SageMath)
@CachedFunction
if n==0: return 1
else: return sum(binomial(n, j)*(-1)^(n-j-1)*((j+2)^3 -1)^(n-j)*a(j) for j in range(n))
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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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STATUS
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approved
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