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%I #36 Dec 29 2019 08:40:34
%S 0,6,3,12,6,30,9,54,18,84,27,126,36,174,51,228,66,294,81,366,102,444,
%T 123,534,144,630,171,732,198,846,225,966,258,1092,291,1230,324,1374,
%U 363,1524,402,1686,441,1854,486,2028,531,2214,576,2406,627
%N Numerators of 1 + n^2/4 + period 3: repeat [-1, 1, 1].
%C First bisection is 3*A008810.
%H Colin Barker, <a href="/A329583/b329583.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (-1,2,3,0,-3,-2,1,1).
%F a(n) = A261327(n) + A131561(n+2) = (n^2 + 4)*(5 - 3*(-1)^n)/8 + (-1)^((n+1) mod 3).
%F From _Colin Barker_, Nov 24 2019: (Start)
%F G.f.: 3*x*(2 + 3*x + x^2 - 2*x^3 + x^4 + 3*x^5 + 2*x^6) / ((1 - x)^3*(1 + x)^3*(1 + x + x^2)).
%F a(n) = -a(n-1) + 2*a(n-2) + 3*a(n-3) - 3*a(n-5) - 2*a(n-6) + a(n-7) + a(n-8) for n>8. (End)
%t MapIndexed[#1 - 2 Boole[Mod[First@ #2, 3] == 1] + 1 &, CoefficientList[Series[(1 + 5 x - x^2 - 2 x^3 + 2 x^4 + 5 x^5)/(1 - x^2)^3, {x, 0, 44}], x]] (* _Michael De Vlieger_, Nov 18 2019 *)
%o (PARI) concat(0, Vec(3*x*(2 + 3*x + x^2 - 2*x^3 + x^4 + 3*x^5 + 2*x^6) / ((1 - x)^3*(1 + x)^3*(1 + x + x^2)) + O(x^40))) \\ _Colin Barker_, Nov 24 2019
%Y Cf. A008810, A042965, A047395, A130823, A131561, A261327.
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Nov 17 2019
%E Incorrect 129 replaced with 123 by _Colin Barker_, Nov 24 2019