A014167 - OEIS

A014167

Partial sums of binary rooted tree numbers.

1, 2, 4, 7, 12, 21, 37, 65, 115, 204, 363, 648, 1158, 2072, 3711, 6649, 11918, 21369, 38321, 68731, 123286, 221157, 396743, 711759, 1276927, 2290903, 4110101, 7373976, 13229809, 23735984, 42585539, 76404333, 137080119, 245941267, 441254017, 791673611

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OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Index entries for sequences related to rooted trees

FORMULA

G.f.: (B(x)-x)/(x(1-x)) where B(x) is g.f. of A002572.

EXAMPLE

G.f. = x + 2*x^2 + 4*x^3 + 7*x^4 + 12*x^5 + 21*x^6 + 37*x^7 + 65*x^8 + 115*x^9 + ...

MAPLE

v:= proc(c, d) option remember; if d<0 or c<0 then 0 elif d=c then 1 else add(v(i, d-c), i=1..2*c) fi end: a:= proc(n) option remember; if n=0 then 0 else a(n-1) +v(1, n) fi end: seq(a(n), n=1..40); # Alois P. Heinz, Aug 22 2008

MATHEMATICA

v[c_, d_] := v[c, d] = If[d<0 || c<0, 0, If[d == c, 1, Sum[v[i, d-c], {i, 1, 2c}]]]; a[n_] := a[n] = If[n == 0, 0, a[n-1]+v[1, n]]; Table[a[n], {n, 1, 29}] (* Jean-François Alcover, Mar 03 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A002572.

Sequence in context: A100671 A189600 A005251 * A103197 A307543 A255062

Adjacent sequences: A014164 A014165 A014166 * A014168 A014169 A014170

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved