%I #33 Feb 21 2020 09:20:40
%S 1,1,1,2,3,5,8,12,18,26,37,51,71,95,128,169,223,289,376,481,617,782,
%T 991,1244,1563,1946,2423,2997,3704,4551,5589,6827,8333,10127,12293,
%U 14866,17959,21619,25996,31166,37318,44563,53153,63240,75153
%N Number of partitions of n in which number of parts is not 2.
%C 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
%C Number of trees with n edges and at most one node of degree > 2. - _Gabriel Burns_, Nov 01 2016
%H Robert Israel, <a href="/A058984/b058984.txt">Table of n, a(n) for n = 0..2000</a>
%H Washington Bomfim, <a href="http://oeis.org/wiki/File:Figura1.png">Star-like trees of 7 edges and correspondent partitions</a>
%H Arnold Knopfmacher, Robert F. Tichy, Stephan Wagner and Volker Ziegler, <a href="http://www.math.tugraz.at/~wagner/GraPartFib.pdf">Graphs, Partitions and Fibonacci Numbers</a> (See Theorem 14.)
%H Stephan Wagner, <a href="http://finanz.math.tu-graz.ac.at/~wagner/Diss.pdf">Graph-theoretical enumeration and digital expansions: an analytic approach</a>, Dissertation, Fakult. f. Tech. Math. u. Tech. Physik, Tech. Univ. Graz, Austria, Feb., 2006.
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F a(n) = p(n) - floor(n/2), where p(n) = number of partitions of n = A000041(n).
%p seq(combinat:-numbpart(n) - floor(n/2), n=0..50); # _Robert Israel_, Nov 07 2016
%t f[n_] := PartitionsP@ n - Floor[n/2]; Array[f, 45, 0]
%o (PARI) a(n) = numbpart(n) - n\2; \\ _Michel Marcus_, Nov 01 2016
%Y Cf. A000041.
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Jan 16 2001