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%I #19 Aug 02 2024 13:31:34
%S 1,1,4,1,16,9,64,25,256,121,1024,441,4096,1849,16384,7225,65536,29241,
%T 262144,116281,1048576,466489,4194304,1863225,16777216,7458361,
%U 67108864,29822521,268435456,119311929,1073741824,477204025,4294967296,1908903481,17179869184
%N a(n) = A112387(n)^2.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,6,0,-8).
%F a(2*n) = A000302(n); a(2*n+1) = A139818(n+1).
%F (a(2*n) + a(2*n-1))^2 = A084175(n+1)^2 + 16*A003683(n)^2, for n >= 1. - _Thomas Scheuerle_, Jun 28 2024
%F G.f. ( 1+x+x^2-2*x^3-2*x^4 ) / ( (x-1)*(2*x+1)*(2*x-1)*(1+x)*(2*x^2+1) ). - _R. J. Mathar_, Aug 02 2024
%t LinearRecurrence[{0, 3, 0, 6, 0, -8}, {1, 1, 4, 1, 16, 9}, 35] (* _Amiram Eldar_, Jul 01 2024 *)
%Y Cf. A000302, A003683, A084175, A112387, A139818.
%K nonn,easy
%O 0,3
%A _Paul Curtz_, Jun 28 2024