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%I #20 Jun 24 2023 13:59:30
%S 1,3,2,-2,-1,5,4,-4,-3,7,6,-6,-5,9,8,-8,-7,11,10,-10,-9,13,12,-12,-11,
%T 15,14,-14,-13,17,16,-16,-15,19,18,-18,-17,21,20,-20,-19,23,22,-22,
%U -21,25,24,-24,-23,27,26,-26,-25,29,28,-28,-27,31,30,-30,-29,33
%N Row sums of triangle A130194.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,-2,2,-1,1).
%F Row sums of A130194, which is composed of A009531 in every column.
%F a(n) = a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4)+a(n-5). - _Colin Barker_, Oct 03 2014
%F G.f.: -x*(x+1)^2/((x-1)*(x^2+1)^2). - _Colin Barker_, Oct 03 2014
%F a(n) = (4+(3+(2*n+1)*(-1)^n)*(-1)^((2*n-3-(-1)^n)/4))/4. - _Luce ETIENNE_, Aug 14 2015
%e a(4) = -2 = sum of A130194 row 4 terms: (-4, -1, 2, 1).
%t LinearRecurrence[{1,-2,2,-1,1},{1,3,2,-2,-1},70] (* _Harvey P. Dale_, Jun 24 2023 *)
%o (PARI) lista(nn) = {vgf = x*(1+x)^2/(1+x^2)^2 + O(x^(nn+1)); m = matrix(nn, nn, i, j, if (i >= j, polcoeff(vgf, i-j+1))); for (n=1, nn, s = sum(k=1, n, m[n, k]); print1(s, ", "););} \\ _Michel Marcus_, Oct 03 2014
%o (PARI) Vec(-x*(x+1)^2/((x-1)*(x^2+1)^2) + O(x^100)) \\ _Colin Barker_, Oct 03 2014
%Y Cf. A130194, A009531.
%K sign,easy
%O 1,2
%A _Gary W. Adamson_, May 16 2007
%E More terms from _Michel Marcus_, Oct 03 2014
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