A038077
Number of rooted identity trees with 2-colored nodes.
Original entry on oeis.org
2, 4, 10, 36, 132, 532, 2222, 9584, 42248, 189776, 864830, 3989656, 18593424, 87413444, 414060796, 1974260912, 9467922870, 45638482068, 221001289714, 1074591477112, 5244497440468, 25681907242416, 126149132242490, 621386729646752, 3068748094479108
Offset: 1
-
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> `if`(n=1, 2, 2*b((n-1)$2)):
seq(a(n), n=1..40); # Alois P. Heinz, May 20 2013
-
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[a[i], j]*b[n - i*j, i-1], {j, 0, n/i}]]];
a[n_] := If[n==1, 2, 2*b[n-1, n-1]];
Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Mar 01 2016, after Alois P. Heinz *)
A038078
Number of identity trees with 2-colored nodes.
Original entry on oeis.org
1, 2, 1, 2, 6, 20, 69, 270, 1026, 4120, 16794, 70230, 298306, 1288912, 5642559, 25007756, 111998920, 506348902, 2308338456, 10602357346, 49026021552, 228085486580, 1067020210339, 5016982766202, 23698640081356, 112422573858292, 535414026652828, 2559204304109868
Offset: 0
-
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(2*b(i-1$2), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> `if`(n=0, 1, 2*b(n-1$2) -2*add(b(j-1$2)*b(n-j-1$2)
, j=1..n-1) -`if`(irem(n, 2, 'r')=0, b(r-1$2), 0)):
seq(a(n), n=0..35); # Alois P. Heinz, Aug 02 2013
-
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[2*b[i-1, i-1], j]*b[n-i*j, i-1], {j, 0, n/i}]]];
a[n_] := If[n==0, 1, 2*b[n-1, n-1] - 2*Sum[b[j-1, j-1]*b[n-j-1, n-j-1], {j, 1, n-1}] - If[Mod[n, 2]==0, r=n/2; b[r-1, r-1], 0]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Mar 01 2016, after Alois P. Heinz *)
A038079
Number of rooted identity trees with 3-colored nodes.
Original entry on oeis.org
3, 9, 36, 192, 1089, 6642, 42129, 275571, 1844028, 12567762, 86924745, 608612814, 4305284400, 30723593751, 220917003516, 1599013642359, 11641144003245, 85186969539435, 626245146267393, 4622806865390823, 34251800667936939, 254640579219212457
Offset: 1
Showing 1-3 of 3 results.
Comments