

A178134


A generalized Lucasbinomial Fibonacci sequence based on A176263: a0=5 a(n)=Sum[A176263[n  m  1, m, a0], {m, 0, Floor[(n  1)/2]}]


0



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
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OFFSET

0,4


COMMENTS

The limiting ratio is (alternating towards):2.7912878474779.
What makes this sequence interesting is that it is based on a generalization of
both Fibonacci types and Lucas binomial Fibonacci types to give
what appears to be a new approach to ratioed sequences.
Both A000800,A004148 are this type of sequence, but where the Narayana (1,3,1)based one has ratio 1+Phi,
the Eulerian (1,4,1) based one never gets a steady ratio limit.
This sequence is an signed {1,4,1} type that gets a steady ratio limit.


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*(16*x^210*x^35*x^4+5*x^5) / ( (x1)*(1+x)*(5*x^2+x1)*(5*x^4+x^21) ).  R. J. Mathar, Nov 05 2012


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}]


CROSSREFS

Cf. A000800, A004148
Sequence in context: A136454 A025522 A019228 * A075121 A075108 A265590
Adjacent sequences: A178131 A178132 A178133 * A178135 A178136 A178137


KEYWORD

uned,sign


AUTHOR

Roger L. Bagula, May 20 2010


STATUS

approved



