A216284 Number of solutions to the equation x^4+y^4 = n with x >= y > 0.

0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

V. Raman, Sep 03 2012

Keywords

• nonn

Examples

			From _Antti Karttunen_, Aug 28 2017: (Start)
For n = 2 there is one solution: 2 = 1^4 + 1^4, thus a(2) = 1.
For n = 17 there is one solution: 17 = 2^4 + 1^4, thus a(17) = 1.
For n = 635318657 we have two solutions: 635318657 = 158^4 + 59^4 = 134^4 + 133^4, thus a(635318657) = 2. Note that this is the first point where the sequence attains value greater than 1. See _Charles R Greathouse IV_'s Jan 12 2017 comment in A216280.
(End)
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A025455, A025446, A000161, A025426, A216280.

Programs

Scheme

(define (A216284 n) (let loop ((x (A255270 n)) (s 0)) (let* ((x4 (A000583 x)) (y4 (- n x4))) (if (< x4 y4) s (loop (- x 1) (+ s (if (and (> y4 0) (= (A000583 (A255270 y4)) y4)) 1 0))))))) ;; Antti Karttunen, Aug 28 2017

Formula

a(n) <= A216280(n). - Antti Karttunen, Aug 28 2017

Extensions

Definition edited to match the given data and the second part of offset (635318657) explicitly added by Antti Karttunen, Aug 28 2017