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%I #10 Apr 25 2021 23:07:25
%S 28,27,117,260,727,1857,4908,12803,33565,87828,229983,602057,1576252,
%T 4126635,10803717,28284452,74049703,193864593,507544140,1328767763,
%U 3478759213,9107509812,23843770287,62423800985,163427632732,427859097147,1120149658773
%N a(n) = F(n+5) * F(n+2) - 12 * (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.
%C First differences of A341928.
%C Second differences of A341208.
%C Third differences of A338225.
%C Fourth differences of A226205.
%C Fourth differences between the areas of consecutive rectangles with side lengths F(n+3) and F(n).
%C Twice the fourth differences between the areas of consecutive deltoids with cross lengths F(n+3) and F(n).
%C Twice the fourth differences between the areas of consecutive triangles with the height and base length are F(n+3) and F(n).
%D B. Muslu, Sayılar ve Bağlantılar, Luna, 2021, p. 52.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-1).
%F a(n) = F(n+5) * F(n+2) - 12 * (-1)^n.
%F G.f.: x*(28 - 29*x + 7*x^2)/(1 - 2*x - 2*x^2 + x^3).
%e For n = 2, a(2) = F(2+5) * F(2+2) - 12 * (-1)^2 = 13 * 3 - 12 = 27.
%t a[n_]:=Fibonacci[n+5]*Fibonacci[n+2]-12(-1)^n
%t Array[a,30] (* _Giorgos Kalogeropoulos_, Apr 02 2021 *)
%Y Cf. A000045, A226205, A338225, A341208, A341928.
%K nonn
%O 1,1
%A _Burak Muslu_, Apr 02 2021
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