cp's OEIS Frontend

A296103 Number of shapes of left-leaning height-balanced AVL trees with n (inner) nodes.

%I A296103 #22 May 31 2019 06:53:09
%S A296103 1,1,1,1,1,2,2,2,3,5,7,9,11,13,17,26,42,66,97,134,180,241,321,424,564,
%T A296103 774,1111,1661,2545,3925,6012,9079,13480,19678,28296,40212,56701,
%U A296103 79599,111469,155795,217301,302590,421396,588782,828633,1178919,1699502,2483695
%N A296103 Number of shapes of left-leaning height-balanced AVL trees with n (inner) nodes.
%C A296103 A left-leaning AVL tree is a binary rooted tree where at any node, the height of left subtree is equal to the height of right subtree or greater by 1.
%H A296103 Alois P. Heinz, <a href="/A296103/b296103.txt">Table of n, a(n) for n = 0..1000</a>
%H A296103 Katarzyna Matylla, <a href="/A296103/a296103.txt">Python program for A296103</a>
%p A296103 B:= proc(x, y, d, a, b) option remember; `if`(a+b<=d,
%p A296103       B(x^2+x*y, x, d, a+b, a)+x, x)
%p A296103     end:
%p A296103 a:= n-> coeff(B(z, 0, n+1, 1, 1), z, n+1):
%p A296103 seq(a(n), n=0..60);  # _Alois P. Heinz_, Dec 05 2017
%t A296103 B[x_, y_, d_, a_, b_] := B[x, y, d, a, b] = If[a + b <= d, B[x^2 + x*y, x, d, a + b, a] + x, x];
%t A296103 a[n_] :=  Coefficient[B[z, 0, n+1, 1, 1], z, n+1];
%t A296103 Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, May 31 2019, after _Alois P. Heinz_ *)
%o A296103 (Python) # see link above
%Y A296103 Cf. A006265.
%K A296103 nonn
%O A296103 0,6
%A A296103 _Katarzyna Matylla_, Dec 04 2017