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A226044 Period of length 8: 1, 64, 16, 64, 4, 64, 16, 64.

%I A226044 #28 Nov 16 2018 22:42:41
%S A226044 1,64,16,64,4,64,16,64,1,64,16,64,4,64,16,64,1,64,16,64,4,64,16,64,1,
%T A226044 64,16,64,4,64,16,64,1,64,16,64,4,64,16,64,1,64,16,64,4,64,16,64,1,64,
%U A226044 16,64,4,64,16,64
%N A226044 Period of length 8: 1, 64, 16, 64, 4, 64, 16, 64.
%C A226044 A002378(n)/A016754(n) gives 0/1, 2/9, 6/25, 12/49, 20/81, 30/121, 42/169, 56/225,..., where A016754(n) = 4*A002378(n) + 1;
%C A226044 A142705(n)/A154615(n+1) gives 0/1, 3/16,  2/9,  15/64,  6/25,  35/144, 12/49,  63/256,..., where A142705(n) = 4*A154615(n+1) + A010685(n);
%C A226044 A061037(n)/A061038(n) gives 0/1, 5/36,  3/16, 21/100, 2/9,   45/196, 15/64,  77/324,..., where A061038(n) = 4*A061037(n) + A177499(n);
%C A226044 A225948(n)/A226008(n) gives 0/1, 9/100, 5/36, 33/196, 3/16,  65/324, 21/100, 105/484,..., where A226008(n) = 4*A225948(n) + a(n).
%C A226044 See also the triangle in Example lines.
%H A226044 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1).
%F A226044 a(n) = A205383(n+7)^2.
%F A226044 G.f.: (1+64*x+16*x^2+64*x^3+4*x^4+64*x^5+16*x^6+64*x^7)/((1-x)*(1+x)*(1+x^2)*(1+x^4)). [_Bruno Berselli_, May 25 2013]
%e A226044 Triangle in which the terms of each line are repeated:
%e A226044 A000012: 1,   ...
%e A226044 A010685: 1,   4,  ...
%e A226044 A177499: 1,  16,  4,  16,  ...
%e A226044 A226044: 1,  64, 16,  64,  4,  64, 16,  64, ...
%e A226044          1, 256, 64, 256, 16, 256, 64, 256, 4, 256, 64, 256, 16, 256, 64, 256, ...
%t A226044 Table[{1, 64, 16, 64, 4, 64, 16, 64}, {7}] // Flatten (* _Jean-François Alcover_, May 24 2013 *)
%Y A226044 Cf. A010685, A177499, A205383, A225948.
%K A226044 nonn,easy
%O A226044 0,2
%A A226044 _Paul Curtz_, May 24 2013