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

1,5

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)

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.

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

Cf. A000196, A338271, A338286.

Sequence in context: A087623 A265260 A363888 * A269243 A036274 A359241

Adjacent sequences: A338265 A338266 A338267 * A338269 A338270 A338271

Keyword

nonn,tabf

Author

Peter Kagey, Oct 19 2020

Status

approved