OFFSET
0,3
COMMENTS
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.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,7,2,-4).
FORMULA
G.f.: x*(1+x)/((1+x-x^2)*(1-2*x-4*x^2));
a(n) = (2^n/3-(-1)^n/3)*(((1+sqrt(5))/2)^(n+1)/sqrt(5)-((1-sqrt(5))/2)^(n+1)/sqrt(5)).
a(n) = a(n-1) + 7*a(n-2) + 2*a(n-3) - 4*a(n-4). - Wesley Ivan Hurt, Sep 04 2022
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 22 2004
STATUS
approved