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A058984
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Number of partitions of n in which number of parts is not 2.
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5
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1, 1, 1, 2, 3, 5, 8, 12, 18, 26, 37, 51, 71, 95, 128, 169, 223, 289, 376, 481, 617, 782, 991, 1244, 1563, 1946, 2423, 2997, 3704, 4551, 5589, 6827, 8333, 10127, 12293, 14866, 17959, 21619, 25996, 31166, 37318, 44563, 53153, 63240, 75153
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refs;
listen;
history;
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internal format)
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OFFSET
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0,4
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COMMENTS
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Number of star-like trees (trees of diameter <= 4) with n edges. Picture of the 12 star-like trees of 7 edges at Bomfim's link. - Washington Bomfim, Feb 13 2011
Number of trees with n edges and at most one node of degree > 2. - Gabriel Burns, Nov 01 2016
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LINKS
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Robert Israel, Table of n, a(n) for n = 0..2000
Washington Bomfim, Star-like trees of 7 edges and correspondent partitions
Arnold Knopfmacher, Robert F. Tichy, Stephan Wagner and Volker Ziegler, Graphs, Partitions and Fibonacci Numbers (See Theorem 14.)
Stephan Wagner, Graph-theoretical enumeration and digital expansions: an analytic approach, Dissertation, Fakult. f. Tech. Math. u. Tech. Physik, Tech. Univ. Graz, Austria, Feb., 2006.
Index entries for sequences related to trees
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FORMULA
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a(n) = p(n) - floor(n/2), where p(n) = number of partitions of n = A000041(n).
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MAPLE
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seq(combinat:-numbpart(n) - floor(n/2), n=0..50); # Robert Israel, Nov 07 2016
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MATHEMATICA
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f[n_] := PartitionsP@ n - Floor[n/2]; Array[f, 45, 0]
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PROG
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(PARI) a(n) = numbpart(n) - n\2; \\ Michel Marcus, Nov 01 2016
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CROSSREFS
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Cf. A000041.
Sequence in context: A173564 A121946 A241823 * A084376 A098693 A122928
Adjacent sequences: A058981 A058982 A058983 * A058985 A058986 A058987
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Jan 16 2001
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STATUS
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approved
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