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%I #22 Mar 29 2024 05:43:14
%S 0,1,3,6,6,5,3,7,12,18,15,11,6,13,21,30,24,17,9,19,30,42,33,23,12,25,
%T 39,54,42,29,15,31,48,66,51,35,18,37,57,78,60,41,21,43,66,90,69,47,24,
%U 49,75,102,78,53,27,55,84,114,87,59,30,61,93,126,96,65,33,67,102
%N n/2 times period 6 sequence [1, 2, 3, 4, 3, 2, ...].
%C A007310 is a subsequence.
%H Bruno Berselli, <a href="/A187601/b187601.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,-2,4,-2,-1,2,-1).
%F a(n) = (n/2)*A028356(n).
%F G.f.: x*(1+x+x^2-x^3+x^4+x^5+x^6)/((1-x)^2*(1+x)^2*(1-x+x^2)^2).
%F a(-n) = -a(n). a(n) = 2*a(n-1)-a(n-2)-2*a(n-3)+4*a(n-4)-2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8) for n>7.
%F a(n) = n*(5-2*(-1)^floor((n+1)/3)-(-1)^n)/4.
%t CoefficientList[Series[x (1 + x + x^2 - x^3 + x^4 + x^5 + x^6) / ((1 - x)^2 (1 + x)^2 (1 - x + x^2)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Aug 19 2013 *)
%t LinearRecurrence[{2,-1,-2,4,-2,-1,2,-1},{0,1,3,6,6,5,3,7},90] (* _Harvey P. Dale_, Aug 20 2017 *)
%o (Magma) [(n/2)*[1, 2, 3, 4, 3, 2][n mod 6 + 1]: n in [0..68]]; /* Other: */ [n*(5-2*(-1)^Floor((n+1)/3)-(-1)^n)/4: n in [0..68]];
%Y Cf. A186813.
%Y Cf. A109044, A088439 (by Superseeker).
%K nonn,look,easy
%O 0,3
%A _Bruno Berselli_, Mar 11 2011
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