cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A124343 Number of rooted trees on n nodes with thinning limbs.

Original entry on oeis.org

1, 1, 2, 3, 6, 10, 21, 38, 78, 153, 314, 632, 1313, 2700, 5646, 11786, 24831, 52348, 111027, 235834, 502986, 1074739, 2303146, 4944507, 10639201, 22930493, 49511948, 107065966, 231874164, 502834328, 1091842824, 2373565195, 5165713137, 11254029616, 24542260010
Offset: 1

Views

Author

Christian G. Bower, Oct 30 2006, suggested by Franklin T. Adams-Watters

Keywords

Comments

A rooted tree with thinning limbs is such that if a node has k children, all its children have at most k children.

Examples

			The a(5) = 6 trees are ((((o)))), (o((o))), (o(oo)), ((o)(o)), (oo(o)), (oooo). - _Gus Wiseman_, Jan 25 2018

Links

Crossrefs

Cf. A000081, A032305, A124344-A124348, A290689, A298303, A298304, A298305, A298422.
Row sums of A244657.

Programs

  • Maple
    b:= proc(n, i, h, v) option remember; `if`(n=0,
      `if`(v=0, 1, 0), `if`(i<1 or v<1 or n A(n$2):
seq(a(n), n=1..35);  # Alois P. Heinz, Jul 08 2014
  • Mathematica
    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, Mar 01 2016, after Alois P. Heinz *)

Extensions

More terms from Alois P. Heinz, Jul 04 2014

A298304 Number of rooted trees on n nodes with strictly thinning limbs.

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 7, 12, 19, 31, 51, 85, 144, 245, 417, 712, 1221, 2091, 3600, 6216, 10763, 18691, 32546, 56782, 99271, 173849, 304877, 535412, 941385, 1657069, 2919930, 5150546, 9093894, 16071634, 28428838, 50331137, 89181251, 158145233, 280650225, 498410197
Offset: 1

Views

Author

Gus Wiseman, Jan 16 2018

Keywords

Comments

An unlabeled rooted tree has strictly thinning limbs if its outdegrees are strictly decreasing from root to leaves.

Examples

			The a(7) = 7 trees: (oo(o(o))), (o(o)(oo)), (ooo(oo)), ((o)(o)(o)), (oo(o)(o)), (oooo(o)), (oooooo).

Links

Crossrefs

Cf. A000081, A001678, A004111, A032305, A124343, A290689, A295461, A298118, A298303, A298305.

Programs

  • Mathematica
    stinctQ[t_]:=And@@Cases[t,b_List:>Length[b]>Max@@Length/@b,{0,Infinity}];
strut[n_]:=strut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1],stinctQ]];
Table[Length[strut[n]],{n,20}]

Extensions

a(26)-a(40) from Alois P. Heinz, Jan 17 2018

A124346 Number of rooted identity trees on n nodes with thinning limbs.

Original entry on oeis.org

1, 1, 1, 2, 2, 4, 6, 11, 17, 32, 56, 102, 184, 340, 624, 1161, 2156, 4036, 7562, 14234, 26828, 50747, 96125, 182545, 347187, 661618, 1262583, 2413275, 4618571, 8850905, 16981142, 32616900, 62713951, 120703497, 232527392, 448344798, 865182999, 1670884073
Offset: 1

Views

Author

Christian G. Bower, Oct 30 2006, suggested by Franklin T. Adams-Watters

Keywords

Comments

A rooted tree with thinning limbs is such that if a node has k children, all its children have at most k children.

Examples

			The a(7) = 6 trees are ((((((o)))))), (o((((o))))), (o(o((o)))), ((o)(((o)))), ((o)(o(o))), (o(o)((o))). - _Gus Wiseman_, Jan 25 2018

Links

Crossrefs

Cf. A000081, A001678, A003238, A004111, A124343-A124348, A276625, A290689, A298303-A298305, A298422.
Row sums of A245120.

Programs

  • Mathematica
    idthinQ[t_]:=And@@Cases[t,b_List:>UnsameQ@@b&&Length[b]>=Max@@Length/@b,{0,Infinity}];
itrut[n_]:=itrut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[itrut/@c]]]/@IntegerPartitions[n-1],idthinQ]];
Table[Length[itrut[n]],{n,25}] (* Gus Wiseman, Jan 25 2018 *)

A298303 Matula-Goebel numbers of rooted trees with thinning limbs.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 39, 40, 42, 44, 45, 46, 48, 49, 50, 52, 54, 55, 56, 58, 60, 62, 63, 64, 65, 66, 69, 70, 72, 75, 76, 77, 78, 80, 81, 84, 86, 87, 88, 90, 91, 92, 93, 94
Offset: 1

Views

Author

Gus Wiseman, Jan 16 2018

Keywords

Comments

An unlabeled rooted tree has thinning limbs if its outdegrees are weakly decreasing from root to leaves.

Crossrefs

Cf. A000081, A007097, A061775, A111299, A124343, A124346, A214577, A276625, A290760, A291636, A298126, A298120, A298304, A298305.

Programs

  • Mathematica
    MGtree[n_]:=If[n===1,{},MGtree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
thinQ[t_]:=And@@Cases[t,b_List:>Length[b]>=Max@@Length/@b,{0,Infinity}];
Select[Range[200],thinQ[MGtree[#]]&]

A298363 Matula-Goebel numbers of rooted identity trees with thinning limbs.

Original entry on oeis.org

1, 2, 3, 5, 6, 10, 11, 15, 22, 26, 30, 31, 33, 39, 55, 58, 62, 65, 66, 78, 87, 93, 94, 110, 127, 130, 141, 143, 145, 155, 158, 165, 174, 186, 195, 202, 235, 237, 254, 274, 282, 286, 290, 303, 310, 319, 330, 334, 341, 377, 381, 390, 395, 403, 411, 429, 435, 465
Offset: 1

Views

Author

Gus Wiseman, Jan 17 2018

Keywords

Comments

An unlabeled rooted tree has thinning limbs if its outdegrees are weakly decreasing from root to leaves.

Examples

			Sequence of trees begins:
1  o
2  (o)
3  ((o))
5  (((o)))
6  (o(o))
10 (o((o)))
11 ((((o))))
15 ((o)((o)))
22 (o(((o))))
26 (o(o(o)))
30 (o(o)((o)))
31 (((((o)))))
33 ((o)(((o))))
39 ((o)(o(o)))
55 (((o))(((o))))
58 (o(o((o))))
62 (o((((o)))))
65 (((o))(o(o)))
66 (o(o)(((o))))
78 (o(o)(o(o)))
87 ((o)(o((o))))
93 ((o)((((o)))))
94 (o((o)((o))))

Crossrefs

Cf. A000081, A004111, A007097, A061775, A111299, A124343, A124346, A214577, A276625, A277098, A290689, A290760, A298304, A298305.

Programs

  • Mathematica
    MGtree[n_]:=If[n===1,{},MGtree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
idthinQ[t_]:=And@@Cases[t,b_List:>UnsameQ@@b&&Length[b]>=Max@@Length/@b,{0,Infinity}];
Select[Range[500],idthinQ[MGtree[#]]&]

Formula

Intersection of A276625 and A298303.
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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