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A378817 Hankel sequence transform of A378816.

%I A378817 #15 Jan 28 2025 08:39:29
%S A378817 -1,-5,6,-10,11,-1,1,17,-18,22,-23,1,-1,-29,30,-34,35,-1,1,41,-42,46,
%T A378817 -47,1,-1,-53,54,-58,59,-1,1,65,-66,70,-71,1,-1,-77,78,-82,83,-1,1,89,
%U A378817 -90,94,-95,1,-1,-101,102,-106,107,-1,1,113,-114,118,-119
%N A378817 Hankel sequence transform of A378816.
%H A378817 Paolo Xausa, <a href="/A378817/b378817.txt">Table of n, a(n) for n = 0..10000</a>
%H A378817 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-3,0,2,0,-1).
%F A378817 G.f.: (-1 - 5*x + 8*x^2 - 4*x^4 + 4*x^5 - x^6 - x^7)/(1 - x^2 + x^4)^2.
%F A378817 a(n) = 2*a(n-2) - 3*a(n-4) + 2*a(n-6) - a(n-8).
%F A378817 a(12*n) = -1.
%F A378817 a(5+12*n) = -1.
%F A378817 a(6+12*n) = 1.
%F A378817 a(11+12*n) = 1.
%F A378817 a(1+12*n) = -5-24*n.
%F A378817 a(2+12*n) = 6+24*n.
%F A378817 a(3+12*n) = -10-24*n.
%F A378817 a(4+12*n) = 11+24*n.
%F A378817 a(7+12*n) = 17+24*n.
%F A378817 a(8+12*n) = -18-24*n.
%F A378817 a(9+12*n) = 22+24*n.
%F A378817 a(10+12*n) = -23-24*n.
%t A378817 LinearRecurrence[{0, 2, 0, -3, 0, 2, 0, -1}, {-1, -5, 6, -10, 11, -1, 1, 17}, 100] (* _Paolo Xausa_, Jan 28 2025 *)
%o A378817 (PARI) a(n) =  (1+(2*n+3-n%3)*((n%6)*((n+1)%6)>0))*(-1)^(n+1+ceil(n/6))
%Y A378817 Cf. A378783, A378816.
%K A378817 sign,easy
%O A378817 0,2
%A A378817 _Thomas Scheuerle_, Dec 08 2024