A126952 - OEIS

%I #11 Dec 15 2019 22:02:33

%S 1,1,5,21,93,421,1937,9017,42349,200277,952425,4549953,21818841,

%T 104966889,506372277,2448641061,11865563853,57604036309,280110716777,

%U 1364092539041,6651682319233,32474171399649,158714415664557

%N a(0)=1, a(n+1) = 5*a(n)-4*A117641(n) for n>=0.

%C Hankel transform is 4^n=A000302(n).

%H Michael De Vlieger, <a href="/A126952/b126952.txt">Table of n, a(n) for n = 0..1001</a>

%H Isaac DeJager, Madeleine Naquin, Frank Seidl, <a href="https://www.valpo.edu/mathematics-statistics/files/2019/08/Drube2019.pdf">Colored Motzkin Paths of Higher Order</a>, VERUM 2019.

%t Block[{$MaxExtraPrecision = 10^3, s = Rest@ CoefficientList[Series[(1 + 3 x - Sqrt[1 - 6 x + 5 x^2])/(2 x^2 + 6 x), {x, 0, 21}], x]}, Nest[Append[#, 5 #[[-1]] - 4 s[[Length@ # - 1]] ] &, {1, 1}, Length@ s]] (* _Michael De Vlieger_, Dec 15 2019, after _Robert G. Wilson v_ at A117641 *)

%Y Cf. A000302, A117641.

%K nonn

%O 0,3

%A _Philippe Deléham_, Mar 19 2007

%E a(11) and a(22) corrected by _Michael De Vlieger_, Dec 15 2019