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A083751
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Number of partitions of n into >= 2 parts and with minimum part >= 2.
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2
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0, 0, 0, 1, 1, 3, 3, 6, 7, 11, 13, 20, 23, 33, 40, 54, 65, 87, 104, 136, 164, 209, 252, 319, 382, 477, 573, 707, 846, 1038, 1237, 1506, 1793, 2166, 2572, 3093, 3659, 4377, 5169, 6152, 7244, 8590, 10086, 11913, 13958, 16423, 19195, 22518, 26251, 30700, 35716
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| Also number of partitions of n such that the largest part is at least 2 and occurs at least twice. Example: a(6)=3 because we have [3,3],[2,2,2] and [2,2,1,1]. - Emeric Deutsch, Mar 29 2006
Also number of partitions of n that contain emergent parts (Cf. A182699). - Omar E. Pol, Oct 21 2011
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..1000
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FORMULA
| a(n) = A000041(n)-A000041(n-1)-1, n>1. - Vladeta Jovovic
G.f.: sum(x^(2j)/product(1-x^i, i=1..j), j=2..infinity). - Emeric Deutsch, Mar 29 2006
a(n) = A002865(n) - 1, n>1. - Omar E. Pol, Oct 21 2011
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EXAMPLE
| a(6) = 3, as 6 = 2+4 = 3+3 = 2+2+2.
a(6) = 3 because 6 = 2+4 = 3+3 = 2+2+2.
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MAPLE
| g:=sum(x^(2*j)/product(1-x^i, i=1..j), j=2..50): gser:=series(g, x=0, 55): seq(coeff(gser, x, n), n=1..51); # Emeric Deutsch, Mar 29 2006
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MATHEMATICA
| Drop[CoefficientList[Series[1/Product[(1-x^k)^1, {k, 2, 50}], {x, 0, 50}], x]-1, 2] or (<<DiscreteMath`Combinatorica`; ) Table[Count[Partitions[n], q_List /; Length[q] > 1 && Min[q] >= 2 ], {n, 24}]
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CROSSREFS
| Cf. A053445, A072380, A008483, A026796, A035989, A036000, A002865, A081094.
Cf. A002865.
First differences of A000094.
Sequence in context: A003879 A078565 A026926 * A034401 A088571 A027187
Adjacent sequences: A083748 A083749 A083750 * A083752 A083753 A083754
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KEYWORD
| nonn
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AUTHOR
| Jon Perry (perry(AT)globalnet.co.uk), Jun 17 2003
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs) and Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 18 2003
Description corrected by James Sellers, Jun 21, 2003
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