A244657
Number T(n,k) of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) k; triangle T(n,k), n>=1, 0<=k<=n-1, read by rows.
Original entry on oeis.org
1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 3, 1, 1, 0, 1, 4, 3, 1, 1, 0, 1, 9, 6, 3, 1, 1, 0, 1, 13, 13, 6, 3, 1, 1, 0, 1, 26, 25, 15, 6, 3, 1, 1, 0, 1, 42, 55, 29, 15, 6, 3, 1, 1, 0, 1, 81, 107, 68, 31, 15, 6, 3, 1, 1, 0, 1, 138, 224, 140, 72, 31, 15, 6, 3, 1, 1
Offset: 1
The A124343(5) = 6 5-node rooted trees with thinning limbs sorted by root outdegree are:
: o : o o o : o : o :
: | : / \ / \ / \ : /|\ : /( )\ :
: o : o o o o o o : o o o : o o o o :
: | : | / \ | | : | : :
: o : o o o o o : o : :
: | : | : : :
: o : o : : :
: | : : : :
: o : : : :
: : : : :
: -1- : ---------2--------- : --3-- : ---4--- :
Thus row 5 = [0, 1, 3, 1, 1].
Triangle T(n,k) begins:
1;
0, 1;
0, 1, 1;
0, 1, 1, 1;
0, 1, 3, 1, 1;
0, 1, 4, 3, 1, 1;
0, 1, 9, 6, 3, 1, 1;
0, 1, 13, 13, 6, 3, 1, 1;
0, 1, 26, 25, 15, 6, 3, 1, 1;
0, 1, 42, 55, 29, 15, 6, 3, 1, 1;
0, 1, 81, 107, 68, 31, 15, 6, 3, 1, 1;
Columns k=0-10 give:
A000007(n-1),
A000012 (for n>1),
A244703,
A244704,
A244705,
A244706,
A244707,
A244708,
A244709,
A244710,
A244711.
-
b:= proc(n, i, h, v) option remember; `if`(n=0,
`if`(v=0, 1, 0), `if`(i<1 or v<1 or n b(n-1$2, k$2):
seq(seq(T(n, k), k=0..n-1), n=1..14);
-
b[n_, i_, h_, v_] := b[n, i, h, v] = If[n == 0, If[v == 0, 1, 0], If[i<1 || v<1 || nJean-François Alcover, Feb 03 2015, after Alois P. Heinz *)
A245142
Number of n-node unlabeled rooted trees with thickening limbs and root outdegree (branching factor) 2.
Original entry on oeis.org
1, 0, 1, 1, 3, 3, 8, 9, 21, 28, 56, 81, 159, 237, 444, 701, 1273, 2060, 3699, 6099, 10840, 18180, 32079, 54417, 95787, 163868, 287914, 496171, 871270, 1509676, 2652068, 4615810, 8114578, 14176261, 24947471, 43718822, 77031659, 135350915, 238791685, 420544851
Offset: 3
A245143
Number of n-node unlabeled rooted trees with thickening limbs and root outdegree (branching factor) 3.
Original entry on oeis.org
1, 0, 0, 1, 1, 1, 3, 3, 5, 9, 12, 17, 32, 42, 64, 106, 157, 232, 379, 563, 866, 1362, 2081, 3186, 5028, 7710, 11924, 18659, 28938, 44842, 70254, 109245, 170266, 266562, 416378, 650513, 1020431, 1597803, 2504070, 3932672, 6174777, 9698203, 15258753, 24005178
Offset: 4
A245144
Number of n-node unlabeled rooted trees with thickening limbs and root outdegree (branching factor) 4.
Original entry on oeis.org
1, 0, 0, 0, 1, 1, 1, 1, 3, 3, 5, 5, 11, 12, 19, 24, 41, 51, 78, 101, 163, 215, 320, 431, 661, 908, 1333, 1846, 2745, 3847, 5630, 7913, 11620, 16481, 23991, 34134, 49782, 71196, 103416, 148178, 215511, 309881, 449941, 647868, 941279, 1358857, 1973315, 2851880
Offset: 5
A245145
Number of n-node unlabeled rooted trees with thickening limbs and root outdegree (branching factor) 5.
Original entry on oeis.org
1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 11, 14, 19, 26, 32, 49, 63, 87, 114, 157, 215, 292, 396, 536, 719, 1002, 1345, 1849, 2496, 3395, 4644, 6344, 8647, 11800, 16049, 21990, 29980, 41087, 56048, 76642, 104863, 143498, 196454, 269057, 368191, 504806
Offset: 6
A245146
Number of n-node unlabeled rooted trees with thickening limbs and root outdegree (branching factor) 6.
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 13, 14, 21, 26, 34, 40, 61, 72, 100, 127, 171, 209, 295, 367, 499, 638, 851, 1083, 1469, 1879, 2512, 3257, 4320, 5576, 7454, 9662, 12833, 16752, 22163, 28874, 38308, 50056, 66232, 86865, 114784, 150429
Offset: 7
A245147
Number of n-node unlabeled rooted trees with thickening limbs and root outdegree (branching factor) 7.
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 13, 16, 21, 28, 34, 42, 52, 70, 85, 113, 141, 185, 227, 290, 371, 474, 602, 771, 983, 1254, 1583, 2038, 2582, 3315, 4217, 5405, 6867, 8783, 11201, 14318, 18285, 23395, 29886, 38207, 48765, 62428
Offset: 8
A245148
Number of n-node unlabeled rooted trees with thickening limbs and root outdegree (branching factor) 8.
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 15, 16, 23, 28, 36, 42, 54, 61, 83, 98, 127, 155, 203, 242, 309, 370, 479, 578, 739, 904, 1155, 1420, 1790, 2194, 2786, 3425, 4323, 5350, 6747, 8362, 10522, 13022, 16397, 20346, 25558
Offset: 9
A245149
Number of n-node unlabeled rooted trees with thickening limbs and root outdegree (branching factor) 9.
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 15, 18, 23, 30, 36, 44, 54, 63, 74, 96, 112, 141, 173, 218, 261, 328, 390, 479, 587, 716, 873, 1080, 1322, 1628, 1998, 2446, 2982, 3677, 4481, 5507, 6744, 8296, 10155, 12521
Offset: 10
A245150
Number of n-node unlabeled rooted trees with thickening limbs and root outdegree (branching factor) 10.
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 17, 18, 25, 30, 38, 44, 56, 63, 76, 87, 110, 126, 159, 188, 237, 280, 348, 410, 503, 588, 726, 854, 1050, 1248, 1534, 1837, 2251, 2694, 3282, 3921, 4784, 5717, 6955
Offset: 11
Showing 1-10 of 11 results.
Comments