

A058984


Number of partitions of n in which number of parts is not 2.


4



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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OFFSET

0,4


COMMENTS

Number of starlike trees (trees of diameter <= 4) with n edges. Picture of the 12 starlike 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


REFERENCES

S. Wagner, Graphtheoretical enumeration and digital expansions: an analytic approach, Dissertation, Fakult. f. Tech. Math. u. Tech. Physik, Tech. Univ. Graz, Austria, Feb., 2006.


LINKS

Robert Israel, Table of n, a(n) for n = 0..2000
W. Bomfim, Starlike 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.)
Index entries for sequences related to trees


FORMULA

a(n) = p(n)  floor(n/2), where p(n) = number of partitions of n = A000041(n).


MAPLE

seq(combinat:numbpart(n)  floor(n/2), n=0..50); # Robert Israel, Nov 07 2016


MATHEMATICA

f[n_] := PartitionsP@ n  Floor[n/2]; Array[f, 45, 0]


PROG

(PARI) a(n) = numbpart(n)  n\2; \\ Michel Marcus, Nov 01 2016


CROSSREFS

Cf. A000041.
Sequence in context: A173564 A121946 A241823 * A084376 A098693 A122928
Adjacent sequences: A058981 A058982 A058983 * A058985 A058986 A058987


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Jan 16 2001


STATUS

approved



