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

0,4

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

Table of n, a(n) for n=0..26.

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: A019228 A361531 A332734 * A369190 A291489 A075121

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