A338268 - OEIS

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

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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