A136793
Number of unlabeled rooted trees with n 4-colored nodes.
Original entry on oeis.org
4, 16, 104, 752, 5996, 50512, 444256, 4027360, 37383044, 353486320, 3393093696, 32976302800, 323839605124, 3208549483216, 32033691247528, 321955764477936, 3254812520854980, 33075467402453872, 337670437247448728, 3461635652745799136, 35620112071990294784
Offset: 1
- F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 293 (4.1.60).
-
with(numtheory):
a:= proc(n) option remember; `if`(n<2, n*4, (add(add(d*
a(d), d=divisors(j))*a(n-j), j=1..n-1))/(n-1))
end:
seq(a(n), n=1..25); # Alois P. Heinz, May 16 2014
-
a[1] = 4; a[n_] := a[n] = Sum[ Sum[ d*a[d], {d, Divisors[j]}]*a[n-j], {j, 1, n-1}]/(n-1); Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Feb 24 2015, after Alois P. Heinz *)
A136796
Number of labeled marked rooted trees with n nodes.
Original entry on oeis.org
2, 16, 288, 8192, 320000, 15925248, 963780608, 68719476736, 5642219814912, 524288000000000, 54394721876836352, 6232805962420322304, 781754012972500385792, 106530593546206374264832, 15672832819200000000000000, 2475880078570760549798248448
Offset: 1
- F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 293 (4.1.60).
A136795
Number of unlabeled marked trees with n nodes.
Original entry on oeis.org
2, 6, 20, 112, 662, 4596, 34032, 268280, 2201634, 18679362, 162611904, 1446148032, 13090979394, 120303384120, 1119971272340, 10544483234056, 100261309326082, 961692928106614, 9296529143261548, 90497666895840376
Offset: 1
- F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 293 (4.1.60).
A384867
Array A(T,k) read down antidiagonals: Number of typed decorated trees of cardinality T on k vertices with D=2 decorations.
Original entry on oeis.org
2, 4, 2, 14, 8, 2, 52, 52, 12, 2, 214, 376, 114, 16, 2, 916, 2998, 1228, 200, 20, 2, 4116, 25256, 14568, 2864, 310, 24, 2, 18996, 222128, 18, 3132, 45140, 5540, 444, 28, 2
Offset: 1
Array starts with rows T=1,2,3.. and columns k=1,2,3.. as
2 4 14 52 214 916 4116 18996
2 8 52 376 2998 25256 222128 2013680
2 12 114 1228 14568 183132 2401410 32465640
2 16 200 2864 45140 754640 13156232 236477200
2 20 310 5540 108930 2272804 49446000 1109081180
2 24 444 9512 224154 5606520 146204792 3930863232
2 28 602 15036 413028 12043500 366122190 11475005616
2 32 784 22368 701768 23373216 811575408 29052861280
2 36 990 31764 1120590 41969844 1638712716 65965167108
2 40 1220 43480 1703710 70875208 3073688160
Showing 1-4 of 4 results.
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