A300649 - OEIS

A300649

Number of same-trees of weight 2n + 1 in which all outdegrees are odd and all leaves greater than 1.

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

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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: A352063 A300650 A363528 * A086599 A371209 A353947

Adjacent sequences: A300646 A300647 A300648 * A300650 A300651 A300652

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 10 2018

STATUS

approved