A317638 a(n) is the number of k with 1 <= k <= n-1 such that a(k)^2 + a(n-k)^2 <= n.

0, 1, 2, 3, 2, 2, 4, 4, 2, 3, 6, 5, 4, 2, 6, 4, 4, 7, 6, 5, 4, 10, 6, 4, 6, 8, 8, 3, 6, 8, 6, 5, 8, 11, 6, 6, 12, 10, 0, 10, 14, 9, 4, 10, 16, 8, 6, 11, 12, 8, 8, 16, 14, 6, 10, 13, 12, 6, 12, 14, 8, 8, 14, 13, 4, 10, 14, 16, 4, 12, 16, 13, 8, 16, 18, 10, 10

Offset

1,3

Comments

See A317582 for similar sequences.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Example

For n = 5:
- a(1)^2 + a(4)^2 = 0^2 + 3^2 = 9 > 5,
- a(2)^2 + a(3)^2 = 1^2 + 2^2 = 5 <= 5,
- a(3)^2 + a(2)^2 = 2^2 + 1^2 = 5 <= 5,
- a(4)^2 + a(1)^2 = 3^2 + 0^2 = 9 > 5,
- hence a(5) = 2.

Mathematica

a[n_] := a[n] = Length@ Select[ Range[n - 1], a[#]^2 + a[n - #]^2 <= n &]; a[0] = 0; Array[a, 80] (* Robert G. Wilson v, Aug 03 2018 *)

Prog

(PARI) a = vector(73); for (n=1, #a, a[n] = sum(k=1, n-1, a[k]^2 + a[n-k]^2 <= n); print1 (a[n] ", "))

Crossrefs

Cf. A317582.

Sequence in context: A337121 A175470 A098534 * A002307 A287707 A029247

Adjacent sequences: A317635 A317636 A317637 * A317639 A317640 A317641

Keyword

nonn,look

Author

Rémy Sigrist, Aug 02 2018

Status

approved