A178134 Sum_{m=0..(n-1)/2} A176263(n-m-1, m).
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
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (1,7,-2,-6,-4,-25,5,25).
Programs
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Maple
A178134 := proc(n) add( A176263(n-m-1,m), m=0..(n-1)/2) ; end proc: # R. J. Mathar, May 15 2016
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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}] -
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
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
Extensions
New name from R. J. Mathar, May 15 2016
Comments