A093122 - OEIS

A093122

a(n) = Jacobsthal(n) * Fibonacci(n+1).

0, 1, 2, 9, 25, 88, 273, 903, 2890, 9405, 30349, 98352, 318045, 1029587, 3331210, 10781001, 34886465, 112897544, 365339961, 1182271695, 3825900650, 12380892261, 40065380357, 129654340704, 419570185125, 1357757761723

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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

Table of n, a(n) for n=0..25.

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) = A001045(n) * A000045(n+1);

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

Cf. A000045, A001045.