The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A144528 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A144528

Triangle read by rows: T(n,k) is the number of trees on n unlabeled nodes with all nodes of degree <= k (n>=1, 0 <= k <= n-1).
(history; published version)

#25 by N. J. A. Sloane at Sun Feb 12 10:22:07 EST 2023

STATUS

proposed

approved

#24 by Robert A. Russell at Sun Feb 05 17:42:33 EST 2023

STATUS

editing

proposed

#23 by Robert A. Russell at Sun Feb 05 17:41:08 EST 2023

MATHEMATICA

b[0, i_, t_, k_] = 1; a = {}; nmax = 1020;

#22 by Robert A. Russell at Sun Feb 05 17:40:11 EST 2023

MATHEMATICA

b[n_, i_, t_, k_] := b[n, i, t, k] = If[i<1, 0, Sum[Binomial[b[i-1, i-1,

k, k] + j-1, j]*b[n-i*j, i-1, t-j, k], {j, 0, Min[t, n/i]}]];

b[0, i_, t_, k_] = 1; a = {}; nmax = 10;

For[ni=2, ni < nmax-1, ni++, (* columns 3 to max-1 *)

gf[x_] = 1 + Sum[b[j-1, j-1, ni, ni] x^j, {j, 1, nmax}];

ci[x_] = SymmetricGroupIndex[ni+1, x] /. x[i_] -> gf[x^i];

a = Append[a, CoefficientList[Normal[Series[

gf[x] - (gf[x]^2 - gf[x^2])/2 + x ci[x], {x, 0, nmax}]], x]]; ]

Join[{1, 0, 1, 0, 0, 1}, Table[Join[{0, 0, 1}, Table[a[[k-3]][[n+1]],

{k, 4, n}]], {n, 4, nmax}]] // Flatten - Robert A. Russell, Feb 05 2023

STATUS

approved

editing

#21 by N. J. A. Sloane at Sat Feb 04 20:58:05 EST 2023

STATUS

proposed

approved

#20 by Robert A. Russell at Sat Feb 04 11:43:18 EST 2023

STATUS

editing

proposed

#19 by Robert A. Russell at Sat Feb 04 11:43:14 EST 2023

LINKS

R. Rebecca Neville, <a href="https://web.archive.org/web/20191029092609/http://gtn.kazlow.info:80/GTN54.pdf">Graphs whose vertices are forests with bounded degree</a>, Graph Theory Notes of New York, LIV (2008), 12-21. [Wayback Machine link]

STATUS

approved

editing

#18 by Peter Luschny at Fri Dec 30 06:34:05 EST 2022

STATUS

reviewed

approved

#17 by Joerg Arndt at Fri Dec 30 02:06:14 EST 2022

STATUS

proposed

reviewed

#16 by Robert A. Russell at Thu Dec 29 16:47:10 EST 2022

STATUS

editing

proposed