cp's OEIS Frontend

A300649 Number of same-trees of weight 2n + 1 in which all outdegrees are odd and all leaves greater than 1.

%I A300649 #7 Mar 10 2018 19:53:30
%S A300649 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,
%T A300649 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,
%U A300649 3,2,3,34,1,3,1,3,390782,1,1,3,3,3,2198,1,1
%N A300649 Number of same-trees of weight 2n + 1 in which all outdegrees are odd and all leaves greater than 1.
%C A300649 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.
%F A300649 a(1) = 1; a(n > 1) = Sum_d a(n/d)^d where the sum is over odd divisors of n greater than 1.
%e A300649 The a(13) = 10 odd same-trees with all leaves greater than 1:
%e A300649 27,
%e A300649 (999),
%e A300649 (99(333)), (9(333)9), ((333)99),
%e A300649 (9(333)(333)), ((333)9(333)), ((333)(333)9),
%e A300649 ((333)(333)(333)), (333333333).
%t A300649 a[n_]:=If[n===1,1,Sum[a[n/d]^d,{d,Select[Rest[Divisors[n]],OddQ]}]];
%t A300649 Table[a[n],{n,1,100,2}]
%o A300649 (PARI) f(n) = if (n==1, 1, sumdiv(n, d, if ((d > 1) && (d % 2), f(n/d)^d)));
%o A300649 a(n) = f(2*n+1); \\ _Michel Marcus_, Mar 10 2018
%Y A300649 Cf. A003238, A006241, A063834, A069283, A273873, A281145, A289078, A289079, A289501, A298118, A300436, A300439, A300574, A300647, A300648, A300650.
%K A300649 nonn
%O A300649 0,5
%A A300649 _Gus Wiseman_, Mar 10 2018