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A143234 a(n) = sqrt(2^(-n)*A004003(n)) mod 32.

%I A143234 #26 Feb 16 2025 08:33:08
%S A143234 1,1,3,29,5,5,7,25,9,9,11,21,13,13,15,17,17,17,19,13,21,21,23,9,25,25,
%T A143234 27,5,29,29,31,1,1,1,3,29,5,5,7,25,9,9,11,21,13,13,15,17,17,17,19,13,
%U A143234 21,21,23,9,25,25,27,5,29,29,31,1,1,1,3,29,5,5,7,25,9,9,11,21,13,13,15,17
%N A143234 a(n) = sqrt(2^(-n)*A004003(n)) mod 32.
%H A143234 G. C. Greubel, <a href="/A143234/b143234.txt">Table of n, a(n) for n = 0..10000</a>
%H A143234 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominoTiling.html">Domino Tiling</a>
%H A143234 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (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).
%F A143234 a(n) = A065072(n) mod 32.
%F A143234 From _G. C. Greubel_, Sep 12 2024: (Start)
%F A143234 a(n) = ( (-1)^A121262(n+1) * A109613(n) ) mod 32.
%F A143234 a(n) = a(n-32). (End)
%t A143234 (* First program *)
%t A143234 a[n_]:= Mod[If[EvenQ[n], n + 1, (-1)^((n-1)/2)*n], 32];
%t A143234 Table[a[n], {n,0,100}]
%t A143234 (* Second program *)
%t A143234 A143234[n_]:= Mod[(-1)^(Floor[Mod[n,4]/3])*(2*Floor[n/2]+1), 32];
%t A143234 Table[A143234[n], {n,0,100}] (* _G. C. Greubel_, Sep 12 2024 *)
%o A143234 (Magma)
%o A143234 A143234:= func< n | (-1)^(0^((n+1) mod 4))*(2*Floor(n/2) + 1) mod 32 >;
%o A143234 [A143234(n): n in [0..100]]; // _G. C. Greubel_, Sep 11 2024
%o A143234 (SageMath)
%o A143234 def A143234(n): return ((-1)^(0^((n+1)%4))*(2*int(n//2)+1))%32
%o A143234 [A143234(n) for n in range(101)] # _G. C. Greubel_, Sep 11 2024
%Y A143234 Cf. A004003, A065072, A109613, A121262.
%K A143234 nonn,easy
%O A143234 0,3
%A A143234 _Eric W. Weisstein_, Jul 31 2008
%E A143234 Offset changed by Editor(s) of Oeis.