A338268 Irregular table read by rows: T(n,k) is the number of compositions of n, b_1 + ... + b_t = n, such that sqrt(b_1 + sqrt(b_2 + ... + sqrt(b_t)...)) = k; 1 <= k <= A000196(n).
1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 0, 2, 0, 6, 0, 0, 0, 2, 0, 8, 0, 0, 0, 4, 0, 12, 0, 2, 0, 0, 6, 0, 0, 18, 0, 2, 0, 0, 8, 0, 0, 26, 0, 2, 0, 0, 14, 0, 0, 40, 0, 4, 0, 0, 20, 0, 0, 60, 0, 6, 0, 0, 28, 0, 2, 0, 88, 0, 8, 0
Offset: 1
Examples
Table begins: n\k| 1 2 3 4 ---+--------- 1 | 1 2 | 0 3 | 0 4 | 0 2 5 | 0 0 6 | 0 2 7 | 0 0 8 | 0 2 9 | 0 0 2 10 | 0 4 0 11 | 0 0 2 12 | 0 6 0 13 | 0 0 2 14 | 0 8 0 15 | 0 0 4 16 | 0 12 0 2 The T(15,3) = 4 compositions of 15 whose iterated sum of square roots equals 3 are: 7 + 2 + 2 + 3 + 1, 7 + 2 + 2 + 4, 6 + 8 + 1, and 6 + 9.
Links
- Peter Kagey, Table of n, a(n) for n = 1..5150 (first 400 rows)
- Code Golf Stack Exchange user Bubbler, The square root of the square root of the square root of the...
- Peter Kagey, Table of first 15^2 = 225 rows.
Formula
T(n,1) = 0 for n > 1.
T(n,k) = 0 if n + k is odd.
Comments