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%I #17 Jul 17 2021 17:06:43
%S 0,1,2,3,8,13,21,55,89,144,377,610,987,2584,4181,6765,17711,28657,
%T 46368,121393,196418,317811,832040,1346269,2178309,5702887,9227465,
%U 14930352,39088169,63245986,102334155,267914296,433494437,701408733,1836311903
%N a(n) = 7*a(n-3) - a(n-6).
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,7,0,0,-1).
%F G.f.: -x*(1+x)*(x^3 - 2*x^2 - x - 1) / ( 1 - 7*x^3 + x^6 ).
%F a(3n) = A033888(n).
%F a(3n+1) = A033890(n).
%F a(3n+2)= A033891(n).
%F a(n) = 2*a(n-1) + a(n-2) if n == 1 (mod 3).
%F a(n) = a(n-1) + a(n-2) if n == 0 (mod 3).
%F a(n) = 2*a(n-1) - a(n-2) if n == 2 (mod 3).
%t a[0] = 0; a[1] = 1;
%t a[n_] := a[n] = If[Mod[n, 3] == 1, 2*a[n - 1] + a[n - 2], If[Mod[n, 3] == 0, a[n - 1] + a[n - 2], 2*a[n - 1] - a[n - 2]]];
%t Table[a[n], {n, 0, 50}]
%t LinearRecurrence[{0,0,7,0,0,-1},{0,1,2,3,8,13},40] (* _Harvey P. Dale_, Jul 17 2021 *)
%Y Cf. A119016, A002965, A002530, A048788.
%K nonn,easy
%O 0,3
%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 28 2008
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