A058984 - OEIS

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

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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