|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
|
|
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)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|