A245747
Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 2.
Original entry on oeis.org
1, 2, 5, 10, 21, 42, 87, 178, 371, 773, 1630, 3447, 7346, 15712, 33790, 72922, 158020, 343494, 749101, 1638102, 3591723, 7893801, 17387930, 38379199, 84875595, 188036829, 417284180, 927469844, 2064465340, 4601670624, 10270463564, 22950838754, 51346678940
Offset: 4
-
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)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 2$2) -b(n-1$2, 1$2):
seq(a(n), n=4..60);
-
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]*b[n-i*j, i-1, t - j, k], {j, 0, Min[t, n/i]}]]];
a[n_] := b[n-1, n-1, 2, 2] - b[n-1, n-1, 1, 1];
Table[a[n], {n, 4, 60}] (* Jean-François Alcover, Aug 28 2021, after Maple code *)
A245748
Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 3.
Original entry on oeis.org
1, 3, 9, 25, 66, 170, 431, 1076, 2665, 6560, 16067, 39219, 95476, 231970, 562736, 1363640, 3301586, 7988916, 19322585, 46722160, 112955614, 273063236, 660116215, 1595906490, 3858740567, 9331539319, 22570697689, 54605064084, 132137719127, 319841444030
Offset: 7
-
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)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 3$2) -b(n-1$2, 2$2):
seq(a(n), n=7..60);
-
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]*b[n - i*j, i-1, t - j, k], {j, 0, Min[t, n/i]}]]];
a[n_] := b[n-1, n-1, 3, 3] - b[n-1, n-1, 2, 2];
Table[a[n], {n, 7, 60}] (* Jean-François Alcover, Aug 28 2021, after Maple code *)
A245749
Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 4.
Original entry on oeis.org
2, 6, 21, 63, 185, 512, 1403, 3750, 9928, 25969, 67462, 174039, 446884, 1142457, 2911078, 7396049, 18746761, 47420345, 119746936, 301941284, 760387426, 1912814031, 4807298905, 12071798139, 30292240853, 75965728619, 190398931985, 476980247827, 1194401725174
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)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 4$2) -b(n-1$2, 3$2):
seq(a(n), n=11..60);
-
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]*b[n - i*j, i-1, t - j, k], {j, 0, Min[t, n/i]}]]];
a[n_] := b[n-1, n-1, 4, 4] - b[n-1, n-1, 3, 3];
Table[a[n], {n, 11, 60}] (* Jean-François Alcover, Aug 28 2021, after Maple code *)
A245750
Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 5.
Original entry on oeis.org
1, 7, 26, 91, 291, 885, 2588, 7373, 20555, 56413, 152812, 409696, 1089029, 2874506, 7542257, 19690939, 51188137, 132579401, 342294012, 881292334, 2263535926, 5801350565, 14840644204, 37901021924, 96650247055, 246137463494, 626087267035, 1590840361215
Offset: 15
-
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)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 5$2) -b(n-1$2, 4$2):
seq(a(n), n=15..60);
-
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]*b[n - i*j, i-1, t-j, k], {j, 0, Min[t, n/i]}]]];
a[n_] := b[n-1, n-1, 5, 5] - b[n-1, n-1, 4, 4];
Table[a[n], {n, 15, 60}] (* Jean-François Alcover, Aug 28 2021, after Maple code *)
A245751
Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 6.
Original entry on oeis.org
3, 15, 70, 256, 884, 2840, 8788, 26238, 76511, 218462, 614003, 1702291, 4667792, 12678438, 34163511, 91424125, 243210889, 643652954, 1695711086, 4449529462, 11634279616, 30324707572, 78819222196, 204348623105, 528597552113, 1364545143938, 3515960193715
Offset: 20
-
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)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 6$2) -b(n-1$2, 5$2):
seq(a(n), n=20..60);
A245752
Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 7.
Original entry on oeis.org
3, 23, 114, 474, 1780, 6179, 20363, 64441, 197653, 591131, 1732165, 4989933, 14171244, 39760411, 110402589, 303808762, 829504935, 2249326273, 6062516975, 16252409052, 43361162336, 115191492778, 304834916107, 803891596292, 2113302899765, 5539657831304
Offset: 25
-
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)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 7$2) -b(n-1$2, 6$2):
seq(a(n), n=25..60);
A245753
Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 8.
Original entry on oeis.org
1, 19, 113, 564, 2362, 9062, 32336, 109826, 358021, 1131089, 3480858, 10484995, 31012892, 90329292, 259621691, 737665484, 2074944123, 5785110380, 16003477783, 43963346701, 120021805899, 325835717520, 880125679307, 2366498068034, 6336725620724, 16903670460151
Offset: 30
-
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)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 8$2) -b(n-1$2, 7$2):
seq(a(n), n=30..60);
A245754
Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 9.
Original entry on oeis.org
6, 63, 400, 2003, 8749, 34754, 128907, 453653, 1531833, 5001990, 15888511, 49313315, 150075356, 449080945, 1324309374, 3855721297, 11100436053, 31641094693, 89395066791, 250570651706, 697347017396, 1928281739720, 5300986280922, 14495618055341, 39446850848309
Offset: 36
-
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)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 9$2) -b(n-1$2, 8$2):
seq(a(n), n=36..70);
A245755
Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 10.
Original entry on oeis.org
15, 147, 1003, 5286, 24396, 101768, 395410, 1452251, 5104104, 17300428, 56912396, 182543809, 573014123, 1765525901, 5352351017, 15996845972, 47213204699, 137795770991, 398168121417, 1140238386377, 3238947787201, 9133172049405, 25582174762816, 71220487524663
Offset: 42
-
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)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 10$2) -b(n-1$2, 9$2):
seq(a(n), n=42..70);
Showing 1-9 of 9 results.