cp's OEIS Frontend

A358650 Matula-Goebel tree number of the binomial tree of n vertices.

%I A358650 #15 Dec 19 2024 11:46:19
%S A358650 1,2,4,6,12,18,42,78,156,234,546,1014,2886,4758,14118,30966,61932,
%T A358650 92898,216762,402558,1145742,1888926,5604846,12293502,28210026,
%U A358650 45860646,121727346,249864654,813198126,1423166394,4740553974,11234495766,22468991532,33703487298
%N A358650 Matula-Goebel tree number of the binomial tree of n vertices.
%C A358650 The top-down definition of the binomial tree suits Matula-Goebel numbering: The tree of n = 2^k + r vertices, for 1 <= r <= 2^k is the binomial tree of 2^k vertices and a child subtree under the root which is the binomial tree of r vertices.
%C A358650 In the tree of n vertices, adding a new singleton child under each vertex gives the tree of 2*n vertices, so that a(2*n) = A348067(a(n)).
%H A358650 Kevin Ryde, <a href="/A358650/b358650.txt">Table of n, a(n) for n = 1..117</a>
%H A358650 Kevin Ryde, <a href="/A358650/a358650.gp.txt">PARI/GP Code</a>
%H A358650 <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%F A358650 a(2^k + r) = a(2^k) * prime(a(r)) for 1 <= r <= 2^k.
%F A358650 a(2^k) = A076146(k+1), being a tree of order k.
%e A358650 The tree of n=13 vertices numbered 0..12 is
%e A358650   0
%e A358650   | \  \    \
%e A358650   1  2  4     8
%e A358650      |  | \   | \  \
%e A358650      3  5  6  9 10  12
%e A358650            |     |
%e A358650            7    11
%e A358650 Vertices 0..7 are the binomial tree of 2^k = 8 vertices, and vertices 8..12 are the binomial tree of 5 vertices.
%e A358650 Using the recurrence, a(13) = a(8 + 5) = a(8) * prime(a(5)) = 78*37 = 2886.
%o A358650 (PARI) \\ See links.
%Y A358650 Cf. A076146, A348067.
%K A358650 nonn,easy
%O A358650 1,2
%A A358650 _Kevin Ryde_, Nov 25 2022