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%I #10 May 15 2016 23:36:09
%S 0,1,1,2,-3,-2,-32,-81,-311,-810,-2515,-6864,-19944,-55043,-156023,
%T -433522,-1217427,-3391226,-9488456,-26462205,-73933535,-206293134,
%U -576040339,-1607642688,-4488069168,-12526662167,-34967630447
%N Sum_{m=0..(n-1)/2} A176263(n-m-1, m).
%C The limiting ratio is (alternating) A222134, 5 times a root of the polynomial 5x^2+x-1 in the denominator of the g.f.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,7,-2,-6,-4,-25,5,25).
%F G.f. -x*(1-6*x^2-10*x^3-5*x^4+5*x^5) / ( (x-1)*(1+x)*(5*x^2+x-1)*(5*x^4+x^2-1) ). - _R. J. Mathar_, Nov 05 2012
%p A178134 := proc(n)
%p add( A176263(n-m-1,m), m=0..(n-1)/2) ;
%p end proc: # _R. J. Mathar_, May 15 2016
%t Clear[a, f, a0, t]
%t f[0, a_] := 0; f[1, a_] := 1;
%t f[n_, a_] := f[n, a] = f[n - 1, a] + a*f[n - 2, a];
%t t[n_, m_, a_] := f[m + 1, a] + f[n + 1 - m, a] - f[n + 1, a];
%t a = 5;
%t a0[n_] := Sum[t[n - m - 1, m, a], {m, 0, Floor[(n - 1)/2]}];
%t Table[a0[n], {n, 0, 30}]
%o (PARI) a(n)=([0,1,0,0,0,0,0,0; 0,0,1,0,0,0,0,0; 0,0,0,1,0,0,0,0; 0,0,0,0,1,0,0,0; 0,0,0,0,0,1,0,0; 0,0,0,0,0,0,1,0; 0,0,0,0,0,0,0,1; 25,5,-25,-4,-6,-2,7,1]^n*[0;1;1;2;-3;-2;-32;-81])[1,1] \\ _Charles R Greathouse IV_, May 15 2016
%Y Cf. A000800, A004148.
%K sign,easy
%O 0,4
%A _Roger L. Bagula_, May 20 2010
%E New name from _R. J. Mathar_, May 15 2016
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