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A260403 Number of unlabeled rooted trees with n nodes where the outdegrees (branching factors) of adjacent nodes differ by at most one. 4
0, 1, 1, 1, 1, 2, 3, 5, 8, 14, 24, 43, 76, 138, 250, 460, 848, 1576, 2939, 5516, 10382, 19629, 37221, 70820, 135097, 258426, 495460, 952083, 1833176, 3536502, 6834408, 13229829, 25649202, 49799891, 96821854, 188485968, 367375883, 716872030, 1400373358 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

EXAMPLE

a(5) = 2:

:    o      o

:    |     / \

:    o    o   o

:    |    |   |

:    o    o   o

:    |

:    o

:    |

:    o

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<v, 0, add(binomial(A(i, h)+j-1, j)*

       b(n-i*j, i-1, h, v-j), j=0..min(n/i, v))))

    end:

A:= proc(n, k) option remember; `if`(n=0, 0,

      add(b(n-1$2, j$2), j=max(k-1, 0)..min(k+1, n-1)))

    end:

a:= n-> add(b(n-1$2, j$2), j=0..n-1):

seq(a(n), n=0..40);

MATHEMATICA

b[n_, i_, h_, v_] := b[n, i, h, v] = If[n==0, If[v==0, 1, 0], If[i<1 || v<1 || n<v, 0, Sum[Binomial[A[i, h]+j-1, j]*b[n-i*j, i-1, h, v-j], {j, 0, Min[n/i, v]}]]]; A[n_, k_] := A[n, k] = If[n==0, 0, Sum[b[n-1, n-1, j, j], {j, Max[k-1, 0], Min[k+1, n-1]}]]; a[n_] := Sum[b[n-1, n-1, j, j], {j, 0, n-1}]; Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Feb 21 2017, translated from Maple *)

CROSSREFS

Cf. A000081, A259863, A260353, A257654, A253244.

Sequence in context: A018154 A114831 A274110 * A127603 A108351 A038495

Adjacent sequences:  A260400 A260401 A260402 * A260404 A260405 A260406

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 24 2015

STATUS

approved

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Last modified March 23 12:43 EDT 2019. Contains 321430 sequences. (Running on oeis4.)