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%I #21 Feb 03 2020 15:19:34
%S 0,4,2,8,4,12,6,16,8,20,10,24,12,28,14,32,16,36,18,40,20,44,22,48,24,
%T 52,26,56,28,60,30,64,32,68,34,72,36,76,38,80,40,84,42,88,44,92,46,96,
%U 48,100,50,104,52,108,54,112,56,116,58,120,60,124,62,128,64,132,66,136
%N a(2n) = 2n, a(2n+1) = 4(n+1).
%C Fourth column of table A210530 for n>0. - _Boris Putievskiy_, Jan 29 2013
%H Harry J. Smith, <a href="/A066104/b066104.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F a(n) = 2*A065423(n+1).
%F O.g.f.: 2*x(2+x)/(1-x^2)^2. - _Len Smiley_, Dec 06 2001
%F a(n) = (3*n+2-(n+2)*(-1)^n)/2. - _Boris Putievskiy_, Jan 29 2013
%t Table[(3*n+2-(n+2)*(-1)^n)/2, {n,0,50}] (* or *) LinearRecurrence[{0, 2, 0, -1}, {0, 4, 2, 8}, 50] (* _G. C. Greubel_, Dec 24 2016 *)
%o (PARI) { for (n=0, 1000, if(n%2, a=2*n + 2, a=n); write("b066104.txt", n, " ", a) ) } \\ _Harry J. Smith_, Nov 14 2009
%o (PARI) concat([0], Vec(2*x*(x+2)/(1-x^2)^2 + O(x^50))) \\ _G. C. Greubel_, Dec 24 2016
%Y Cf. A065423, A210530.
%K easy,nonn
%O 0,2
%A _George E. Antoniou_, Dec 04 2001
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