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A142881 a(0) = 0, a(1) = 1, after which, if n=3k: a(n) = 2*a(n-1) - a(n-2), if n=3k+1: a(n) = a(n-1) + a(n-2), if n=3k+2: a(n) = 2*a(n-1) + a(n-2).

%I A142881 #23 Jan 30 2016 07:48:56
%S A142881 0,1,2,3,5,13,21,34,89,144,233,610,987,1597,4181,6765,10946,28657,
%T A142881 46368,75025,196418,317811,514229,1346269,2178309,3524578,9227465,
%U A142881 14930352,24157817,63245986,102334155,165580141,433494437,701408733,1134903170
%N A142881 a(0) = 0, a(1) = 1, after which, if n=3k: a(n) = 2*a(n-1) - a(n-2), if n=3k+1: a(n) = a(n-1) + a(n-2), if n=3k+2: a(n) = 2*a(n-1) + a(n-2).
%C A142881 The original name of the sequence was: A modulo three switched recursion (third kind): a(n)=If[Mod[n, 3] ==2, 2*a(n - 1) + a(n - 2), If[Mod[n, 3] == 1, a(n - 1) + a(n - 2), 2*a(n - 1) - a(n - 2)]].
%C A142881 How is this related to A000045 ? - _Antti Karttunen_, Jan 29 2016
%H A142881 Antti Karttunen, <a href="/A142881/b142881.txt">Table of n, a(n) for n = 0..120</a>
%H A142881 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,7,0,0,-1).
%F A142881 a(n) = If[Mod[n, 3] == 2, 2*a(n - 1) + a(n - 2), If[Mod[n, 3] == 1, a(n - 1) + a(n - 2), 2*a(n - 1) - a(n - 2)]].
%F A142881 a(n) = 7*a(n-3)-a(n-6). G.f.: -x^2*(x^4+2*x^3-3*x^2-2*x-1) / (x^6-7*x^3+1). [_Colin Barker_, Jan 08 2013]
%F A142881 a(0) = 0, a(1) = 1, after which, if n is a multiple of 3, a(n) = 2*a(n-1) - a(n-2), else, if n is of the form 3k+1, a(n) = a(n-1) + a(n-2), and otherwise [when n is of the form 3k+2], a(n) = 2*a(n-1) + a(n-2). - _Antti Karttunen_, Jan 29 2016, after the original name of the sequence.
%t A142881 Clear[a, n]; a[0] = 0; a[1] = 1; a[n_] := a[n] = If[Mod[n, 3] == 2, 2*a[n - 1] + a[n - 2], If[Mod[n, 3] == 1, a[n - 1] + a[n - 2], 2*a[n - 1] - a[n - 2]]]; b = Table[a[n], {n, 0, 50}]
%o A142881 (Scheme, with memoization-macro definec)
%o A142881 (definec (A142881 n) (cond ((<= n 1) n) ((= 0 (modulo n 3)) (- (* 2 (A142881 (- n 1))) (A142881 (- n 2)))) ((= 1 (modulo n 3)) (+ (A142881 (- n 1)) (A142881 (- n 2)))) (else (+ (* 2 (A142881 (- n 1))) (A142881 (- n 2))))))
%o A142881 ;; _Antti Karttunen_, Jan 29 2016
%o A142881 (PARI) a=vector(100); a[1]=1; a[2]=2; for(n=3, #a, if(n%3==0, a[n]=2*a[n-1]-a[n-2], if(n%3==1, a[n]=a[n-1]+a[n-2], a[n]=2*a[n-1]+a[n-2]))); concat(0, a) \\ _Colin Barker_, Jan 30 2016
%Y A142881 Cf. A000045, A119016, A002965, A002530, A048788.
%K A142881 nonn,easy
%O A142881 0,3
%A A142881 _Roger L. Bagula_ and _Gary W. Adamson_, Sep 28 2008
%E A142881 Offset corrected and sequence edited by _Antti Karttunen_, Jan 29 2016