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

A124344 Number of ordered rooted trees on n nodes with thinning limbs.

Original entry on oeis.org

1, 1, 2, 4, 10, 25, 68, 187, 530, 1523, 4447, 13121, 39107, 117490, 355507, 1082234, 3312255, 10185125, 31450633, 97480337, 303157086, 945671951, 2958113722, 9276528602, 29158191215, 91845796986, 289874628176, 916536727561
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.

Links

Crossrefs

Cf. A000108, A124343-A124348.
Row sums of A124328.

Formula

G.f.: A(x) = A0(x)+A1(x)+A2(x)+... where A0(x)=x, An(x) = x*(A0(x)+A1(x)+...+An(x))^n.

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 *)

A124345 Number of mobiles (circular rooted trees) on n nodes with thinning limbs.

Original entry on oeis.org

1, 1, 2, 3, 6, 10, 24, 47, 113, 258, 624, 1492, 3694, 9090, 22753, 57111, 144541, 367243, 938449, 2406720, 6198045, 16013447, 41507254, 107887092, 281170859, 734518306, 1923119062, 5045423169, 13262334340, 34923020733, 92113656841
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.

Crossrefs

Cf. A032200, A124343-A124348.

A124347 Number of labeled rooted trees on n nodes with thinning limbs.

Original entry on oeis.org

1, 2, 9, 52, 425, 4266, 52507, 754944, 12499209, 233296030, 4852006181, 111149993736, 2781312439633, 75460291482772, 2206445155886805, 69163853027437216, 2313709581153992033, 82271226298253976054
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.

Crossrefs

Cf. A000169, A124343-A124348.
Showing 1-5 of 5 results.

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

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