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%I #6 Oct 25 2020 02:38:47
%S 1,1,3,1,3,5,7,3,5,7,9,5,7,9,11,7,9,11,13,9,11,13,15,11,13,15,17,13,
%T 15,17,19,15,17,19,21,17,19,21,23,19,21,23,25,21,23,25,27,23,25,27,29,
%U 25,27,29,31,27,29,31,33,29,31,33,35,31,33,35,37,33,35,37,39
%N First differences of A326118.
%C It includes exclusively all the odd numbers (A005408). Except for 1, 3 and 5 that appear three times, each other odd number appears four times.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F O.g.f.: (1 + 2*x^2 - 2*x^3 + x^4 + 2*x^5 - 2*x^7)/((1 - x)^2*(1 + x + x^2 + x^3)).
%F E.g.f.: (3*exp(-x) + exp(x)*(7 + 2*x) - 6*cos(x) + 6*sin(x))/4 - 2*x - x^2.
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n > 7.
%F a(n) = (7 + 2*n - 6*cos(n*Pi/2) + 3*(-1)^n + 6*sin(n*Pi/2))/4 for n > 2.
%t LinearRecurrence[{1,0,0,1,-1},{1,1,3,1,3,5,7,3},71]
%Y Cf. A004277 (averages of the increasing runs), A005408, A326118.
%K nonn,easy
%O 0,3
%A _Stefano Spezia_, Oct 23 2020
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