A093045 - OEIS

%I #8 Jun 13 2015 00:51:19

%S 0,0,2,4,18,50,176,546,1806,5780,18810,60698,196704,636090,2059174,

%T 6662420,21562002,69772930,225795088,730679922,2364543390,7651801300,

%U 24761784522,80130760714,259308681408,839140370250,2715515523446

%N 2*Jacobsthal(n-1)*Fibonacci(n).

%C Form a graph from a triangle and its midpoint triangle. A093045 counts walks of length n between a vertex of the original triangle and the opposite vertex of the midpoint triangle.

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

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

%F a(n) = 2*A001045(n-1)*A000045(n);

%F a(n) = 2(2^n/6+(-1)^n/3)(((1+sqrt(5))/2)^n/sqrt(5)-((1-sqrt(5))/2)^n/sqrt(5)).

%F a(n) = 2*A093122(n-1). - _R. J. Mathar_, Dec 17 2014

%K easy,nonn

%O 0,3

%A _Paul Barry_, Mar 22 2004