A216284 - OEIS

%I #15 Aug 28 2017 09:22:25

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A216284/b216284.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) <= A216280(n). - _Antti Karttunen_, Aug 28 2017

%e From _Antti Karttunen_, Aug 28 2017: (Start)

%e For n = 2 there is one solution: 2 = 1^4 + 1^4, thus a(2) = 1.

%e For n = 17 there is one solution: 17 = 2^4 + 1^4, thus a(17) = 1.

%e 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.

%e (End)

%o (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

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

%K nonn

%O 1,635318657

%A _V. Raman_, Sep 03 2012

%E Definition edited to match the given data and the second part of offset (635318657) explicitly added by _Antti Karttunen_, Aug 28 2017