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A216284
Number of solutions to the equation x^4+y^4 = n with x >= y > 0.
4
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
1,635318657
LINKS
FORMULA
a(n) <= A216280(n). - Antti Karttunen, Aug 28 2017
EXAMPLE
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)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
V. Raman, Sep 03 2012
EXTENSIONS
Definition edited to match the given data and the second part of offset (635318657) explicitly added by Antti Karttunen, Aug 28 2017
STATUS
approved