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.

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

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• eigen
• look

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

Crossrefs

Cf. A003238, A007562.

Cf. A027750.

Programs

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

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 *)

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

Extensions

New description from Christian G. Bower, Oct 15 1998