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a(n) = 8*(n + floor(n/3)) - 3; second column of A347834.
4

%I #18 Dec 24 2024 02:42:44

%S 5,13,29,37,45,61,69,77,93,101,109,125,133,141,157,165,173,189,197,

%T 205,221,229,237,253,261,269,285,293,301,317,325,333,349,357,365,381,

%U 389,397,413,421,429,445,453,461,477,485,493

%N a(n) = 8*(n + floor(n/3)) - 3; second column of A347834.

%H Paolo Xausa, <a href="/A347836/b347836.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).

%F a(n) = A347834(n, 1) = A178415(A265667(n), 2), for n >= 1.

%F a(n) = ((3*A047529(n) + 1)*4 - 1)/3 = ((3*(n + floor(n/3)) - 1)*8 - 1)/3 = ((A319451(n) - 1)*8 - 1)/3, for n >= 1.

%F O.g.f.: G(x) = (-3 + 8*x + 8*x^2 + 19*x^3)/((1 - x)*(1 - x^3)), with a(0) = -3.

%p seq(8*(n + floor(n/3)) - 3, n = 1..47); # _Peter Luschny_, Oct 10 2021

%t A347836[n_] := 8*(n + Floor[n/3]) - 3; Array[A347836, 50] (* or *)

%t LinearRecurrence[{1, 0, 1, -1}, {5, 13, 29, 37}, 50] (* _Paolo Xausa_, Feb 27 2024 *)

%Y Cf. A047529 (first column), A178415, A265667, A319451, A347834, A347837 (third column).

%K nonn,easy

%O 1,1

%A _Wolfdieter Lang_, Oct 07 2021