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

Author

N. J. A. Sloane, Jan 16 2001

Keywords

• nonn

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

Crossrefs

Cf. A000041.

Programs

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]

PARI

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

Formula

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