A007439 Number of planted trees: all sub-rooted trees from any node are identical; non-root, non-leaf nodes an even distance from the root are of degree 2. (Formerly M0301)

1, 1, 1, 2, 2, 4, 3, 7, 4, 11, 6, 15, 7, 24, 8, 29, 12, 40, 13, 51, 14, 68, 19, 76, 20, 107, 23, 116, 29, 147, 30, 175, 31, 215, 39, 229, 45, 297, 46, 312, 55, 387, 56, 435, 57, 513, 73, 534, 74, 670, 78, 705, 92, 823, 93, 897, 102, 1051, 117, 1082

Offset

1,4

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n=1..1000

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

Formula

a(n+2) = Sum a(k), k|n. Shifts left two places under inverse Moebius transformation.

G.f. A(x) satisfies: A(x) = x + x^2 * (1 + A(x) + A(x^2) + A(x^3) + ...). - Ilya Gutkovskiy, May 09 2019

Mathematica

a[n_] := a[n] = Sum[a[k], {k, Divisors[n-2]}]; a[1] = a[2] = 1; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, May 15 2013 *)

Prog

(Haskell)
a007439 n = a007439_list !! (n-1)
a007439_list = 1 : 1 : f 2 where
   f x = (sum $ map a007439 $ a027750_row (x - 1)) : f (x + 1)
-- Reinhard Zumkeller, Dec 20 2014

Crossrefs

Cf. A003238, A007562.

Cf. A027750.

Sequence in context: A336305 A265701 A353747 * A238622 A096441 A100824

Adjacent sequences: A007436 A007437 A007438 * A007440 A007441 A007442

Keyword

nonn,nice,eigen,look

Author

N. J. A. Sloane

Extensions

New description from Christian G. Bower, Oct 15 1998

Status

approved