A379972 -id:A379972 - cp's OEIS frontend

A380203 With given points 0,1 on the x-axis, a(n) is the number of ways to construct n with m circles where 2^(m-1)

1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 2, 4, 1, 2, 1, 1, 5, 9, 6, 10, 4, 8, 4, 8, 1, 4, 2, 4, 1, 2, 1, 1, 15, 28, 15, 31, 13, 25, 14, 28, 10, 19, 11, 22, 8, 15, 9, 17, 2, 8, 4, 12, 2, 8, 4, 8, 1, 4, 2, 4, 1, 2, 1, 1, 50, 94, 56, 99, 45, 91, 51, 97, 39, 74, 41, 92, 31, 74, 40, 85, 26, 61

Offset: 1

Gerhard Kirchner, Jan 16 2025

nonn

Description of the construction: The first circle with center 1 and radius 1 intersects the x-axis at 2. The center of the next circle is 2. Each circle, except for the last one, intersects the axis at the center of the next one. The last circle intersects the axis at x.
The sequence of indices with a(n)=1 is A379972. Further comments on the construction can be found there. The algorithm generates a tree. In this section, a(6)=2 and a(n)=1 otherwise.
        5
       /
      3
     / \
  1-2   6
     \ /
      4-7
       \
        8

			 n a(n)  intersection points on the x-axis
 5  1    2, 3, 5
 6  2    2, 3, 6 or 2, 4, 6
10  4    2, 3, 5, 10 or 2, 3, 6, 10 or 2, 4, 6, 10 or 2, 4, 7, 10

Cf. A379972.

block(m:7, aa:makelist(i-1,i,1,m+2), freq:makelist(0,i,1,2^m),
recursion(t):=  (freq[aa[t]] : freq[aa[t]] + 1,
 if t< m+2 then
   for k from t-1 thru 1 step -1 do
     (p:2*aa[t] - aa[k] ,
     if p> 2^(t-2) then (aa[t+1]:p, recursion(t+1) ) ) ) ,
 recursion(2), freq );

cp's OEIS Frontend

A380203 With given points 0,1 on the x-axis, a(n) is the number of ways to construct n with m circles where 2^(m-1)

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