The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A298478 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A298478

Number of unlabeled rooted trees with n nodes in which all positive outdegrees are different.
(history; published version)

#15 by Alois P. Heinz at Tue Feb 02 18:20:53 EST 2021

STATUS

proposed

approved

#14 by Andrew Howroyd at Tue Feb 02 18:19:34 EST 2021

STATUS

editing

proposed

#13 by Andrew Howroyd at Tue Feb 02 16:17:21 EST 2021

COMMENTS

a(n) is the number of labeled trees with sum of the labels equal to n-1 and the outdegree of every node less than or equal to the value of its label. - Andrew Howroyd, Feb 02 2021

#12 by Andrew Howroyd at Tue Feb 02 16:04:45 EST 2021

DATA

1, 1, 1, 3, 3, 5, 13, 15, 23, 34, 95, 106, 176, 241, 374, 942, 1129, 1760, 2515, 3711, 5136, 12857, 14911, 23814, 33002, 49141, 65798, 97056, 209707, 255042, 389725, 545290, 790344, 1071010, 1525919, 2043953, 4272124, 5110583, 7772247, 10611491, 15447864, 20496809

LINKS

Andrew Howroyd, <a href="/A298478/b298478.txt">Table of n, a(n) for n = 1..100</a>

PROG

(PARI)

relabel(b)={my(w=hammingweight(b)); b = bitand((1<<w)-1, b); b + (((1 << (w-hammingweight(b))) - 1) << w)}

a(n)={local(M=Map());

my(recurse(b, k) = if(!b, 1, b=relabel(b); my(hk=[b, k], z); if(!mapisdefined(M, hk, &z),

z = if(k==0,

sum(i=1, logint(b, 2), if(bittest(b, i), self()(b-2^i, i-1))),

sum(f=2^logint(b, 2), b, if(!bitnegimply(f, b), self()(f, 0)*self()(b-f, k-1)));

);

mapput(M, hk, z)); z));

if( n==1, 1, my(t=0); for(np=1, sqrtint(2*n-2), forpart(p=n-1-binomial(np, 2), t+=recurse(sum(i=1, #p, 2^(p[i]+i-1)), 0), , [np, np])); t);

} \\ Andrew Howroyd, Feb 02 2021

KEYWORD

nonn,more

nonn

EXTENSIONS

Terms a(35) and beyond from Andrew Howroyd, Feb 02 2021

STATUS

approved

editing

#11 by Alois P. Heinz at Sat Jan 20 11:18:37 EST 2018

STATUS

editing

approved

#10 by Alois P. Heinz at Sat Jan 20 11:18:35 EST 2018

EXTENSIONS

a(27) - a(34) from Robert G. Wilson v, Jan 19 2018

STATUS

approved

editing

#9 by Peter Luschny at Sat Jan 20 02:39:17 EST 2018

STATUS

reviewed

approved

#8 by Robert G. Wilson v at Fri Jan 19 19:39:50 EST 2018

STATUS

proposed

reviewed

#7 by Robert G. Wilson v at Fri Jan 19 19:39:40 EST 2018

STATUS

editing

proposed

#6 by Robert G. Wilson v at Fri Jan 19 19:39:36 EST 2018

DATA

1, 1, 1, 3, 3, 5, 13, 15, 23, 34, 95, 106, 176, 241, 374, 942, 1129, 1760, 2515, 3711, 5136, 12857, 14911, 23814, 33002, 49141, 65798, 97056, 209707, 255042, 389725, 545290, 790344, 1071010

EXTENSIONS

a(27) - a(34) from Robert G. Wilson v, Jan 19 2018

STATUS

proposed

editing