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Search: id:A070047
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| A070047 |
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Number of partitions of n in which no part appears more than twice and no two parts differ by 1. |
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+0
4
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| 1, 1, 2, 1, 3, 3, 5, 5, 8, 8, 12, 12, 19, 19, 27, 28, 39, 41, 55, 58, 77, 82, 106, 113, 145, 156, 196, 210, 262, 283, 348, 376, 459, 497, 600, 651, 781, 849, 1009, 1097, 1298, 1413, 1660, 1807, 2113, 2302, 2676, 2916, 3377, 3681, 4242, 4623, 5309, 5787, 6619
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Euler transform of period 6 sequence [1,1,-1,1,1,0,...].
Coefficients in expansion of permanent of infinite tridiagonal matrix: matrix([[1, x, 0, 0, 0, ...], [1+x, 1, x^2, 0, 0, ...], [0, 1+x^2, 1, x^3, 0, ...], [0, 0, 1+x^3, 1, x^4, ...], ...]). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 18 2004
Number of partitions of n into non-multiples of 3 in which no two parts differ by 1 (see the Andrews-Lewis reference). Example: a(6)=5 because we have 51,42,411,222,111111. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 19 2008
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REFERENCES
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G. E. Andrews and R. P. Lewis, An algebraic identity of F. H. Jackson ..., Discrete Math., 232 (2001), 77-83.
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FORMULA
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G.f.: Prod_{n>0} ((1-q^(6n-3))^2 (1-q^(6n))/(1-q^n)) = q^(1/24)eta(q^3)^2/(eta(q)eta(q^6)); eta = Dedekind's function.
G.f.: Prod_{n>0}[(1-q^(6n-3))/[(1-q^(3n-2))(1-q^(3n-1))]]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 19 2008
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EXAMPLE
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a(6)=5 because we have 6,51,42,411,33.
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PROGRAM
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(PARI) a(n)=local(q); if(n<1, n==0, q=x+x*O(x^n); polcoeff(eta(q^3)^2/eta(q)/eta(q^6), n))
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CROSSREFS
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Sequence in context: A026927 A074500 A107237 this_sequence A101198 A034394 A058689
Adjacent sequences: A070044 A070045 A070046 this_sequence A070048 A070049 A070050
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KEYWORD
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nonn
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AUTHOR
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njas, May 09 2002
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EXTENSIONS
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Additional comments from Michael Somos, Dec 04 2002
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