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A138879
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Sum of parts of the outer shell of the partitions of n.
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40
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1, 3, 5, 11, 15, 31, 39, 71, 94, 150, 196, 308, 389, 577, 750, 1056, 1353, 1881, 2380, 3230, 4092, 5412, 6821, 8935, 11150, 14386, 17934, 22834, 28281, 35735, 43982, 55066, 67551, 83821, 102365, 126267, 153397, 188001, 227645, 277305, 334383
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OFFSET
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1,2
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COMMENTS
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Row sums of the triangles A135010, A138121, A138151 and others related to the shell model of partitions (see A135010 and A138121).
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LINKS
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Table of n, a(n) for n=1..41.
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FORMULA
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a(n) = A000041(n)*n - A000041(n-1)*(n-1) = A138880(n) + A000041(n-1).
a(n) = A066186(n) - A066186(n-1), for n>1.
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EXAMPLE
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For n=6 the a(6)=31 because the parts of the outer shell of the partitions of 6 are (6),(3,3),(4,2),(2,2,2),(1),(1),(1),(1),(1),(1),(1), so the sum is a(6) = 6+3+3+4+2+2+2+2+1+1+1+1+1+1+1 = 31. See the illustrations in A135010.
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MAPLE
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A066186 := proc(n) n*combinat[numbpart](n) ; end proc:
A138879 := proc(n) A066186(n)-A066186(n-1) ; end proc:
seq(A138879(n), n=1..80) ; # R. J. Mathar, Jan 27 2011
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CROSSREFS
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Cf. A000041, A066186, A133041, A135010, A138121, A138135 - A138138, A138151, A138880, A139100.
Sequence in context: A164053 A200176 A092929 * A018313 A219039 A074820
Adjacent sequences: A138876 A138877 A138878 * A138880 A138881 A138882
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KEYWORD
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nonn
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AUTHOR
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Omar E. Pol, Apr 30 2008
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EXTENSIONS
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a(34) corrected by R. J. Mathar, Jan 27 2011
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STATUS
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approved
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