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A227380 Doubling the first two of every four nonnegative numbers.

%I A227380 #24 Nov 03 2024 05:02:26
%S A227380 0,2,2,3,8,10,6,7,16,18,10,11,24,26,14,15,32,34,18,19,40,42,22,23,48,
%T A227380 50,26,27,56,58,30,31,64,66,34,35,72,74,38,39,80,82,42,43,88,90,46,47,
%U A227380 96,98,50,51,104,106,54,55,112,114
%N A227380 Doubling the first two of every four nonnegative numbers.
%C A227380 a(n) and its differences:
%C A227380   0,    2,  2,   3,   8,  10,   6,   7,  16,...
%C A227380   2,    0,  1,   5,   2,  -4,   1,   9,   2,...
%C A227380   -2,   1,  4,  -3,  -6,   5,   8,  -7, -10,...   see A103889(n)
%C A227380   3,    3, -7,  -3,  11,   3, -15,  -3,  19,...
%C A227380   0,  -10,  4,  14,  -8, -18,  12,  22, -16,...
%C A227380   -10, 14, 10,- 22, -10,  30,  10, -38, -10,... .
%C A227380 The inverse binomial transform is
%C A227380 b(n)=0, 2, -2, 3, 0, -10, 24, -28, 0, 72, -160, 176, 0,...
%C A227380     =(0, 1, -1, 1, 0, -1, 4, -4, 0, 4, -16, 16, 0,...) * a(n).
%H A227380 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-3,4,-3,2,-1).
%F A227380 a(n) = n*A130658(n+2) = 2*A227316(n)/(n+1).
%F A227380 a(n) - a(n-4) = period 4:repeat 8, 8, 4, 4 = 4*A130658(n+2).
%F A227380 G.f.: (x^5 + 5*x^3 - 2*x^2 + 2*x)/((1-x)^2 * (1+x^2)^2). - _Ralf Stephan_, Jul 13 2013
%t A227380 {2#[[1]],2#[[2]],#[[3]],#[[4]]}&/@Partition[Range[0,60],4]//Flatten (* or *) LinearRecurrence[{2,-3,4,-3,2,-1},{0,2,2,3,8,10},60] (* _Harvey P. Dale_, Dec 14 2021 *)
%Y A227380 Cf. A001477.
%K A227380 nonn,easy
%O A227380 0,2
%A A227380 _Paul Curtz_, Jul 09 2013