A244403
Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 7.
Original entry on oeis.org
1, 2, 6, 17, 50, 143, 416, 1198, 3467, 10019, 29001, 83945, 243228, 705012, 2044935, 5934425, 17231410, 50058023, 145491836, 423056364, 1230683672, 3581556220, 10427172296, 30368394833, 88476965536, 257860132679, 751756288476, 2192311994070, 6395199688864
Offset: 8
-
b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 7$2) -`if`(k=0, 0, b(n-1$2, 6$2)):
seq(a(n), n=8..40);
-
b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, 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]}]] // FullSimplify] ; a[n_] := b[n - 1, n - 1, 7, 7] - If[n == 0, 0, b[n - 1, n - 1, 6, 6]]; Table[a[n], {n, 8, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)
A244404
Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 8.
Original entry on oeis.org
1, 2, 6, 17, 50, 143, 416, 1199, 3473, 10042, 29089, 84259, 244316, 708679, 2057087, 5974077, 17359390, 50467157, 146789962, 427148444, 1243513350, 3621591235, 10551595959, 30753712080, 89666493709, 261522175986, 763002239120, 2226771020793, 6500575182332
Offset: 9
-
b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 8$2) -`if`(k=0, 0, b(n-1$2, 7$2)):
seq(a(n), n=9..40);
-
b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, 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]}]] // FullSimplify] ; a[n_] := b[n - 1, n - 1, 8, 8] - If[n == 0, 0, b[n - 1, n - 1, 7, 7]]; Table[a[n], {n, 9, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)
A244405
Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 9.
Original entry on oeis.org
1, 2, 6, 17, 50, 143, 416, 1199, 3474, 10048, 29112, 84347, 244630, 709767, 2060754, 5986231, 17399060, 50595235, 147199567, 428448576, 1247613511, 3634451971, 10591746511, 30878554201, 90053295475, 262716880036, 766682072349, 2238077375703, 6535237181868
Offset: 10
-
b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 9$2) -`if`(k=0, 0, b(n-1$2, 8$2)):
seq(a(n), n=10..45);
-
b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, 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]}]] // FullSimplify] ; a[n_] := b[n - 1, n - 1, 9, 9] - If[n == 0, 0, b[n - 1, n - 1, 8, 8]]; Table[a[n], {n, 10, 45}] (* Jean-François Alcover, Feb 09 2015, after Maple *)
A244406
Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 10.
Original entry on oeis.org
1, 2, 6, 17, 50, 143, 416, 1199, 3474, 10049, 29118, 84370, 244718, 710081, 2061842, 5989898, 17411214, 50634907, 147327663, 428858279, 1248914115, 3638554143, 10604615353, 30918735919, 90178253585, 263104102071, 767878267996, 2241762411780, 6546561427512
Offset: 11
-
b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 10$2) -`if`(k=0, 0, b(n-1$2, 9$2)):
seq(a(n), n=11..40);
-
b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, 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]}]] // FullSimplify] ; a[n_] := b[n - 1, n - 1, 10, 10] - If[n == 0, 0, b[n - 1, n - 1, 9, 9]]; Table[a[n], {n, 11, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)