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A257654 Number of unlabeled rooted trees with n nodes where the outdegrees (branching factors) of adjacent nodes differ by exactly one. 4
0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 2, 0, 1, 3, 3, 1, 2, 6, 6, 3, 6, 11, 11, 9, 15, 23, 24, 25, 39, 48, 52, 67, 96, 107, 122, 174, 242, 247, 295, 448, 598, 598, 744, 1141, 1493, 1493, 1913, 2898, 3730, 3826, 5003, 7362, 9396, 9980, 13201, 18757, 23840 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,14

COMMENTS

These trees are also counted by A260353 and A260403.

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) = 1:     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(`if`(j=k, 0,

      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..60);

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[If[j==k, 0, 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, 60}] (* Jean-Fran├žois Alcover, Feb 21 2017, translated from Maple *)

CROSSREFS

Cf. A000081, A259863, A260353, A260403, A253244.

Sequence in context: A185287 A276554 A297323 * A167637 A109754 A220074

Adjacent sequences:  A257651 A257652 A257653 * A257655 A257656 A257657

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 25 2015

STATUS

approved

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Last modified February 21 16:28 EST 2018. Contains 299414 sequences. (Running on oeis4.)