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A300649 Number of same-trees of weight 2n + 1 in which all outdegrees are odd and all leaves greater than 1. 3
1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 3, 1, 2, 10, 1, 1, 3, 3, 1, 3, 1, 1, 62, 1, 2, 3, 1, 3, 3, 1, 1, 158, 3, 1, 3, 1, 1, 254, 3, 1, 1514, 1, 3, 3, 1, 3, 3, 3, 1, 2078, 1, 1, 2461, 1, 1, 3, 1, 3, 8222, 3, 2, 3, 34, 1, 3, 1, 3, 390782, 1, 1, 3, 3, 3, 2198, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A same-tree of weight n > 0 is either a single node of weight n, or a finite sequence of two or more same-trees whose weights are all equal and sum to n.

LINKS

Table of n, a(n) for n=0..75.

FORMULA

a(1) = 1; a(n > 1) = Sum_d a(n/d)^d where the sum is over odd divisors of n greater than 1.

EXAMPLE

The a(13) = 10 odd same-trees with all leaves greater than 1:

27,

(999),

(99(333)), (9(333)9), ((333)99),

(9(333)(333)), ((333)9(333)), ((333)(333)9),

((333)(333)(333)), (333333333).

MATHEMATICA

a[n_]:=If[n===1, 1, Sum[a[n/d]^d, {d, Select[Rest[Divisors[n]], OddQ]}]];

Table[a[n], {n, 1, 100, 2}]

PROG

(PARI) f(n) = if (n==1, 1, sumdiv(n, d, if ((d > 1) && (d % 2), f(n/d)^d)));

a(n) = f(2*n+1); \\ Michel Marcus, Mar 10 2018

CROSSREFS

Cf. A003238, A006241, A063834, A069283, A273873, A281145, A289078, A289079, A289501, A298118, A300436, A300439, A300574, A300647, A300648, A300650.

Sequence in context: A232529 A095374 A300650 * A086599 A181846 A305499

Adjacent sequences:  A300646 A300647 A300648 * A300650 A300651 A300652

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 10 2018

STATUS

approved

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Last modified July 9 04:34 EDT 2020. Contains 335538 sequences. (Running on oeis4.)