The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A220819

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A220819

Number of rooted binary leaf-multilabeled trees with n leaves on the label set [2].
(history; published version)

#17 by OEIS Server at Sat Sep 07 12:26:03 EDT 2019

LINKS

Alois P. Heinz, <a href="/A220819/b220819_1.txt">Table of n, a(n) for n = 1..1542</a> (first 200 terms from Andrew Howroyd)

#16 by Alois P. Heinz at Sat Sep 07 12:26:03 EDT 2019

STATUS

editing

approved

Discussion

Sat Sep 07

12:26

OEIS Server: Installed new b-file as b220819.txt.  Old b-file is now b220819_1.txt.

#15 by Alois P. Heinz at Sat Sep 07 12:25:55 EDT 2019

CROSSREFS

Column k=2 of A319541.

#14 by Alois P. Heinz at Sat Sep 07 12:24:44 EDT 2019

LINKS

Andrew Howroyd, Alois P. Heinz, <a href="/A220819/b220819_1.txt">Table of n, a(n) for n = 1..1542</a> (first 200</a> terms from Andrew Howroyd)

#13 by Alois P. Heinz at Sat Sep 07 12:17:11 EDT 2019

MAPLE

b:= proc(n, k) option remember; `if`(n<2, k*n, `if`(n::odd, 0,

(t-> t*(1-t)/2)(b(n/2, k)))+add(b(i, k)*b(n-i, k), i=1..n/2))

end:

a:= n-> b(n, 2)-2*b(n, 1):

seq(a(n), n=1..40); # Alois P. Heinz, Sep 07 2019

STATUS

proposed

editing

#12 by Jean-François Alcover at Sat Sep 07 11:37:14 EDT 2019

STATUS

editing

proposed

#11 by Jean-François Alcover at Sat Sep 07 11:37:10 EDT 2019

MATHEMATICA

(* b = A083563 *) b[n_] := b[n] = If[n < 2, 2*n, If[OddQ[n], 0, #*(1 - #)/2 &[b[n/2]]]] + Sum[b[i]*b[n - i], {i, 1, n/2}];

(* c = A001190 *) c[n_?OddQ] := c[n] = Sum[c[k]*c[n - k], {k, 1, (n - 1)/2}]; c[n_?EvenQ] := c[n] = Sum[c[k]*c[n - k], {k, 1, n/2 - 1}] + (1/2)*c[n/2]*(1 + c[n/2]); c[0] = 0; c[1] = 1;

a[n_] := b[n] - 2 c[n];

Array[a, 27] (* Jean-François Alcover, Sep 07 2019 *)

STATUS

approved

editing

#10 by N. J. A. Sloane at Sun Sep 23 22:32:27 EDT 2018

STATUS

proposed

approved

#9 by Andrew Howroyd at Sun Sep 23 19:35:13 EDT 2018

STATUS

editing

proposed

#8 by Andrew Howroyd at Sun Sep 23 19:17:39 EDT 2018

DATA

0, 1, 4, 14, 48, 171, 614, 2270, 8518, 32567, 126168, 495079, 1962752, 7853581, 31672502, 128622480, 525523990, 2158818376, 8911039462, 36941520279, 153740822408, 642085403709, 2690217364606, 11304538078369, 47630350694248, 201181246749072, 851690546714230

LINKS

Andrew Howroyd, <a href="/A220819/b220819.txt">Table of n, a(n) for n = 1..200</a>

V. P. Johnson, <a href="http://wwwpeople.math.sc.edu/~czabarka/Theses/JohnsonThesis.pdf">Enumeration Results on Leaf Labeled Trees</a>, Ph. D. Dissertation, Univ. Southern Calif., 2012.

FORMULA

a(n) = A083563(n) - 2*A001190(n). - Andrew Howroyd, Sep 23 2018

CROSSREFS

Column 2 of A319541.

Cf. A001190, A083563.

EXTENSIONS

Terms a(11) and beyond from Andrew Howroyd, Sep 23 2018

STATUS

approved

editing