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A092285
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Number of productions of a certain ``divide-and-conquer'' context-free grammar in Chomsky normal form that generates all permutations of n symbols.
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1
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1, 4, 12, 22, 65, 116, 399, 554, 2475, 3232, 14938, 20208, 101413, 130846, 691890, 924946, 4867559, 6281552, 35154066, 46902128
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| P. R. J. Asveld, Generating all permutations by context-free grammars in Chomsky normal form, Theoretical Computer Science 354 (2006) 118-130.
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FORMULA
| a(n) = Sum(k=1..n, t(n, k)*C(k, ceiling[k/2])), where t(n, k) is the n-th row in the Pascal-like triangle of A090349 and C(k, i) is the binomial coefficient.
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EXAMPLE
| a(4) = 4*C(1,1) + 6*C(2,1) + 0*C(3,2) + 1*C(4,2) = 4 + 12 + 0 + 6 = 22; cf. the example grammar in A090349.
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CROSSREFS
| Cf. A090349.
Sequence in context: A008161 A008243 A008194 * A016440 A008010 A047957
Adjacent sequences: A092282 A092283 A092284 * A092286 A092287 A092288
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KEYWORD
| nonn
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AUTHOR
| Peter R. J. Asveld (infprja(AT)cs.utwente.nl), Jan 30 2004
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