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A Jacobsthal Fibonacci product.
1

%I #7 Aug 26 2019 13:23:40

%S 1,0,4,6,30,80,286,882,2924,9350,30438,98208,318278,1029210,3331820,

%T 10780014,34888062,112894960,365344142,1182264930,3825911596,

%U 12380874550,40065409014,129654294336,419570260150,1357757640330

%N A Jacobsthal Fibonacci product.

%C Form a graph from a triangle and its midpoint triangle. A093121 counts closed walks of length n at a vertex of the midpoint triangle in this configuration.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,7,2,-4).

%F G.f.: (1-x-3x^2)/((1+x-x^2)(1-2x-4x^2));

%F a(n)=A078008(n)*A000045(n+1);

%F a(n)=(2^n/3+2(-1)^n/3)(((1+sqrt(5))/2)^(n+1)/sqrt(5)-((1-sqrt(5))/2)^(n+1)/sqrt(5)).

%t LinearRecurrence[{1,7,2,-4},{1,0,4,6},30] (* _Harvey P. Dale_, Aug 26 2019 *)

%K easy,nonn

%O 0,3

%A _Paul Barry_, Mar 22 2004