A058984 Number of partitions of n in which number of parts is not 2.

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

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