%I #8 Sep 04 2022 22:47:19
%S 0,1,2,9,25,88,273,903,2890,9405,30349,98352,318045,1029587,3331210,
%T 10781001,34886465,112897544,365339961,1182271695,3825900650,
%U 12380892261,40065380357,129654340704,419570185125,1357757761723
%N a(n) = Jacobsthal(n) * Fibonacci(n+1).
%C Form a graph from a triangle and its midpoint triangle. This sequence counts walks of length n between two vertices 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.: x*(1+x)/((1+x-x^2)*(1-2*x-4*x^2));
%F a(n) = A001045(n) * A000045(n+1);
%F a(n) = (2^n/3-(-1)^n/3)*(((1+sqrt(5))/2)^(n+1)/sqrt(5)-((1-sqrt(5))/2)^(n+1)/sqrt(5)).
%F a(n) = a(n-1) + 7*a(n-2) + 2*a(n-3) - 4*a(n-4). - _Wesley Ivan Hurt_, Sep 04 2022
%t CoefficientList[Series[x*(1 + x)/((1 + x - x^2)*(1 - 2*x - 4*x^2)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Sep 04 2022 *)
%Y Cf. A000045, A001045.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Mar 22 2004