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%I #21 May 29 2021 19:58:34
%S 0,1,1,4,7,25,46,163,301,1066,1969,6973,12880,45613,84253,298372,
%T 551131,1951765,3605158,12767239,23582713,83515378,154263517,
%U 546305929,1009096480,3573595369,6600884809,23376249796,43178904223,152912962465,282449675134,1000261987867,1847611013269,6543095027674
%N a(n) = a(n-1) + 3*a(n-2) if n is even, otherwise a(n) = 3*a(n-1) + a(n-2), a(0)=0, a(1)=1.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,7,0,-3).
%F G.f.: x*(1 + x - 3*x^2)/(1 - 7*x^2 + 3*x^4).
%F a(n) = 7*a(n-2) - 3*a(n-4).
%F a(n) = (2 - (-1)^n)*a(n-1) + (2 + (-1)^n)*a(n-2) for n > 1, a(0)=0, a(1)=1.
%F a(2k) = A190972(k).
%t LinearRecurrence[{0, 7, 0, -3}, {0, 1, 1, 4}, 34]
%t RecurrenceTable[{a[0] == 0, a[1] == 1, a[n] == (2 - (-1)^n) a[n - 1] + (2 + (-1)^n) a[n - 2]}, a, {n, 33}]
%o (PARI) concat(0, Vec(x*(1+x-3*x^2)/(1-7*x^2+3*x^4) + O(x^99))) \\ _Altug Alkan_, Aug 27 2016
%Y Cf. A005824, A010684, A079162, A190972.
%K nonn,easy
%O 0,4
%A _Ilya Gutkovskiy_, Aug 27 2016
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