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 A178134 Sum_{m=0..(n-1)/2} A176263(n-m-1, m). 1
 0, 1, 1, 2, -3, -2, -32, -81, -311, -810, -2515, -6864, -19944, -55043, -156023, -433522, -1217427, -3391226, -9488456, -26462205, -73933535, -206293134, -576040339, -1607642688, -4488069168, -12526662167, -34967630447 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The limiting ratio is (alternating) A222134, 5 times a root of the polynomial 5x^2+x-1 in the denominator of the g.f. LINKS Index entries for linear recurrences with constant coefficients, signature (1,7,-2,-6,-4,-25,5,25). FORMULA 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 MAPLE A178134 := proc(n)     add( A176263(n-m-1, m), m=0..(n-1)/2) ; end proc: # R. J. Mathar, May 15 2016 MATHEMATICA Clear[a, f, a0, t] f[0, a_] := 0; f[1, a_] := 1; f[n_, a_] := f[n, a] = f[n - 1, a] + a*f[n - 2, a]; t[n_, m_, a_] := f[m + 1, a] + f[n + 1 - m, a] - f[n + 1, a]; a = 5; a0[n_] := Sum[t[n - m - 1, m, a], {m, 0, Floor[(n - 1)/2]}]; Table[a0[n], {n, 0, 30}] PROG (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 CROSSREFS Cf. A000800, A004148. Sequence in context: A136454 A025522 A019228 * A075121 A075108 A265590 Adjacent sequences:  A178131 A178132 A178133 * A178135 A178136 A178137 KEYWORD sign,easy AUTHOR Roger L. Bagula, May 20 2010 EXTENSIONS New name from R. J. Mathar, May 15 2016 STATUS approved

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