This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A226976 #26 Jun 30 2025 15:52:50
%S A226976 1,9,28,133,539,2322,9773,41501,175636,744273,3152359,13354306,
%T A226976 56568617,239630337,1015087436,4299984173,18215017507,77160064914,
%U A226976 326855259829,1384581132277,5865179743556,24845300179929,105246380344463,445830821750018,1888569667033489
%N A226976 Fibonacci(n)^3 + Fibonacci(n+2)^3.
%H A226976 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,6,-3,-1).
%F A226976 a(n) = 3a(n-1)+6a(n-2)-3a(n-3)-a(n-4)
%F A226976 G.f.: (1+6x-5x^2-2x^3)/(1-3x-6x^2+3x^3+x^4)= (2x^2+7x+1)(1-x)/((x^2-x-1)(x^2+4x-1))
%e A226976 a(2) = Fibonacci(2)^3 + Fibonacci(4)^3 = 1^3 + 2^3 = 9
%t A226976 Table[Fibonacci[n]^3 + Fibonacci[n+2]^3,{n,0,50}]
%t A226976 #[[1]]+#[[3]]&/@Partition[Fibonacci[Range[0,30]]^3,3,1] (* or *) LinearRecurrence[{3,6,-3,-1},{1,9,28,133},30] (* _Harvey P. Dale_, Jun 30 2025 *)
%o A226976 (PARI) a(n) = fibonacci(n)^3+fibonacci(n+2)^3; \\ _Joerg Arndt_, Jul 07 2013
%Y A226976 Cf. A000045 (Fibonacci), A056570 (Fibonacci^3).
%Y A226976 Cf. A110224 (Fib(n)^3 + Fib(n+1)^3).
%K A226976 nonn
%O A226976 0,2
%A A226976 _Ron Knott_, Jun 27 2013