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A058984 Number of partitions of n in which number of parts is not 2. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

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

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

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Last modified March 2 06:48 EST 2021. Contains 341744 sequences. (Running on oeis4.)