login
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).
3
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
1,5
COMMENTS
For any fixed c, T(x^2 + c, x) = T(y^2 + c, y) for sufficiently large integers x and y. See A338286.
T(n,k) <= A338286(n - k^2).
LINKS
Peter Kagey, Table of n, a(n) for n = 1..5150 (first 400 rows)
FORMULA
T(n,1) = 0 for n > 1.
T(n,k) = 0 if n + k is odd.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Peter Kagey, Oct 19 2020
STATUS
approved