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A302773 Numerators of (3*n + 2)/12.

%I A302773 #35 Sep 08 2022 08:46:21
%S A302773 1,5,2,11,7,17,5,23,13,29,8,35,19,41,11,47,25,53,14,59,31,65,17,71,37,
%T A302773 77,20,83,43,89,23,95,49,101,26,107,55,113,29,119,61,125,32,131,67,
%U A302773 137,35,143,73,149,38,155,79,161,41,167,85,173,44,179,91,185,47,191,97
%N A302773 Numerators of (3*n + 2)/12.
%C A302773 Or numerators of (3*n+2)/4. - _Altug Alkan_, Apr 17 2018
%H A302773 Colin Barker, <a href="/A302773/b302773.txt">Table of n, a(n) for n = 0..1000</a>
%H A302773 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).
%F A302773 G.f.: (1 + 5*x + 2*x^2 + 11*x^3 + 5*x^4 + 7*x^5 + x^6 + x^7)/((1 - x)^2*(1 + x)^2*(1 + x^2)^2).
%F A302773 a(n) = 2*a(n-4) - a(n-8).
%F A302773 a(n) = (3*n + 2)*(((-1)^n + 1)*(i^(n*(n+1)) - 5) + 16)/16, where i = sqrt(-1).
%F A302773 a(n) = A016789(n)/A109008(n+2).
%t A302773 Table[Numerator[(3 n + 2)/12], {n, 0, 70}]
%t A302773 LinearRecurrence[{0,0,0,2,0,0,0,-1},{1,5,2,11,7,17,5,23},80] (* _Harvey P. Dale_, Feb 04 2021 *)
%o A302773 (PARI) vector(70, n, n--; numerator((3*n+2)/12))
%o A302773 (PARI) Vec((1 + 5*x + 2*x^2 + 11*x^3 + 5*x^4 + 7*x^5 + x^6 + x^7)/((1 - x)^2*(1 + x)^2*(1 + x^2)^2) + O(x^60)) \\ _Colin Barker_, Apr 16 2018
%o A302773 (Sage) [numerator((3*n+2)/12) for n in (0..70)]
%o A302773 (GAP) List([0..70], n -> NumeratorRat((3*n+2)/12));
%o A302773 (Magma) [Numerator((3*n+2)/12): n in [0..70]];
%Y A302773 Cf. A016789, A109008.
%Y A302773 Cf. A060819: numerators of n/4, with n > 0.
%Y A302773 Cf. A176672: numerators of (3*n + 1)/12.
%Y A302773 First bisection is A165355; second bisection is A016969.
%K A302773 nonn,easy,frac
%O A302773 0,2
%A A302773 _Bruno Berselli_, Apr 13 2018