closed form for A007501
Brendan McKay
bdm at cs.anu.edu.au
Wed Jan 31 13:29:10 CET 2001
%I A007501 M0818
%S A007501 2,3,6,21,231,26796,359026206,64449908476890321,
%T A007501 2076895351339769460477611370186681,
%U A007501 2156747150208372213435450937462082366919951682912789656986079991221
%N A007501 a(n+1) = a(n)*(a(n)+1)/2.
%D A007501 W. H. Cutler, Subdividing a Box into Completely Incongruent Boxes, J. Rec. Math., 12 (1979), 104-111.
%o A007501 (PARI) a(n)=if(n<1,2,a(n-1)*(1+a(n-1))/2)
%t A007501 f[n_Integer] := n(n + 1)/2; NestList[f, 2, 10]
%K A007501 nonn,easy,huge
%O A007501 0,1
%A A007501 njas, Robert G. Wilson v (rgwv at kspaint.com)
I haven't looked at that reference, so I don't know if the following
alternative description is equivalent:
The number of nonisomorphic complete binary trees
with leaves coloured using two colours.
Example for depth 2:
o
/ \
/ \
o o
/ \ / \
/ \ / \ The nonisomorpic possibilites are
A B B B AAAA, AAAB, AABB, ABAB, ABBB, BBBB.
My real question: is there a closed form for this sequence?
Brendan.
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