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%I #13 Mar 11 2016 23:04:44
%S 4,10,16,22,28,34,40,46,52,58,64,70,76,82,83,84,88,94,100,106,112,118,
%T 124,130,136,142,148,154,160,166,172,178,179,180,184,190,196,202,208,
%U 214,220,226,232,238,244,250,256,262,268,274,275,276,280,286,292,298,304,310,316,322,328,334,335
%N Integers n such that the n-th golden rectangle number is the sum of 4 but no fewer nonzero squares.
%C Golden rectangle numbers equal the partial sums of squares of Fibonacci numbers.
%C Corresponding golden rectangle numbers are 15, 4895, 1576239, 507544127, 163427632719, 52623190191455, ...
%H Chai Wah Wu, <a href="/A269960/b269960.txt">Table of n, a(n) for n = 1..10000</a>
%e 4 is a term because 1^2 + 1^2 + 2^2 + 3^2 = 3*5 = x^2 + y^2 + z^2 has no solution for integer x, y and z.
%e 5 is not a term because 1^2 + 1^2 + 2^2 + 3^2 + 5^2 = 5*8 = 2^2 + 6^2.
%o (PARI) isA004215(n)= my(fouri, j) ; fouri=1 ; while( n >=7*fouri, if( n % fouri ==0, j= n/fouri-7 ; if( j % 8==0, return(1) ) ; ); fouri *= 4 ; ) ; return(0) ;
%o a001654(n) = fibonacci(n)*fibonacci(n+1);
%o for(n=1, 1e3, if(isA004215(a001654(n)), print1(n, ", ")));
%Y Cf. A001654, A004215, A016957.
%K nonn
%O 1,1
%A _Altug Alkan_, Mar 08 2016
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