A358074 a(n) is the number of distinct ways n can be written as the sum of a perfect square and factorial.

1, 2, 1, 0, 1, 2, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,2

Comments

This does not count x^2 and (-x)^2 as distinct, nor does it count 0! and 1! as distinct.

Links

Table of n, a(n) for n=1..100.

Example

2 = 0^2 + 2! = 1^2 + 1!, so a(2) = 2.

Mathematica

With[{f = Range[5]!}, a[n_] := Count[f, _?(IntegerQ @ Sqrt[n - #] &)]; Array[a, f[[-1]]]] (* Amiram Eldar, Oct 30 2022 *)

Crossrefs

Cf. A000142, A000290.

Sequence in context: A298247 A035148 A155077 * A170968 A114114 A090787

Adjacent sequences: A358071 A358072 A358073 * A358075 A358076 A358077

Keyword

nonn

Author

Walter Robinson, Oct 29 2022

Status

approved