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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)
16
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).
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. A027750.
Sequence in context: A336305 A265701 A353747 * A238622 A096441 A100824
KEYWORD
nonn,nice,eigen,look
EXTENSIONS
New description from Christian G. Bower, Oct 15 1998
STATUS
approved