The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A038060

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A038060

Number of trees with 3-colored nodes.
(history; published version)

#16 by Alois P. Heinz at Sun Nov 01 07:46:27 EST 2020

STATUS

proposed

approved

#15 by Jean-François Alcover at Sun Nov 01 07:04:43 EST 2020

STATUS

editing

proposed

#14 by Jean-François Alcover at Sun Nov 01 07:04:40 EST 2020

MATHEMATICA

b[n_] := b[n] = If[n < 2, 3n, (Sum[Sum[b[d] d, {d, Divisors[j]}] b[n - j], {j, 1, n - 1}])/(n - 1)];

a[n_] := If[n == 0, 1, b[n] - (Sum[b[k] b[n - k], {k, 0, n}] - If[Mod[n, 2] == 0, b[n/2], 0])/2];

a /@ Range[0, 25] (* Jean-François Alcover, Nov 01 2020, after Alois P. Heinz in A006965 *)

STATUS

approved

editing

#13 by Alois P. Heinz at Wed Jun 03 15:27:51 EDT 2020

STATUS

editing

approved

#12 by Alois P. Heinz at Wed Jun 03 15:27:47 EDT 2020

DATA

1, 3, 6, 18, 75, 342, 1773, 9894, 58596, 362061, 2314119, 15185223, 101830986, 695253993, 4819762446, 33851833506, 240472935735, 1725315714729, 12487872432924, 91097741283408, 669227023979088, 4947500029023540, 36786363204267282, 274949933519917908

STATUS

approved

editing

#11 by Jon E. Schoenfield at Sat Dec 19 12:21:46 EST 2015

STATUS

editing

approved

#10 by Jon E. Schoenfield at Sat Dec 19 12:21:44 EST 2015

FORMULA

G.f.: B(x) - B^2(x)/2 + B(x^2)/2, where B(x) is g.f. for A038059.

AUTHOR

Christian G. Bower, Jan 04 1999.

STATUS

approved

editing

#9 by Russ Cox at Fri Mar 30 17:37:06 EDT 2012

AUTHOR

_Christian G. Bower (bowerc(AT)usa.net), _, Jan 04 1999.

Discussion

Fri Mar 30

17:37

OEIS Server: https://oeis.org/edit/global/178

#8 by Russ Cox at Sun Jul 10 18:21:30 EDT 2011

LINKS

<a href="/Sindx_index/Tra.html#trees">Index entries for sequences related to trees</a>

Discussion

Sun Jul 10

18:21

OEIS Server: https://oeis.org/edit/global/91

#7 by N. J. A. Sloane at Thu Nov 11 07:34:06 EST 2010

LINKS

<a href="/Sindx_Tra.html#trees">Index entries for sequences related to trees</a>

KEYWORD

nonn,new

nonn