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 A032441 #15 Jul 08 2025 19:36:43
%S A032441 1,2,2,4,7,16,37,92,232,596,1541,4006,10441,27262,71254,186356,487579,
%T A032441 1276004,3339821,8742472,22885996,59912932,156848617,410626154,
%U A032441 1075018897,2814412826,7368190922,19290113572,50502074767,132215989336,346145696821,906220783316
%N A032441 a(n) = Sum_{i=0..2} binomial(Fibonacci(n),i).
%H A032441 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-6,4,2,-1).
%F A032441 a(0)=1, a(1)=2, a(2)=2, a(3)=4, a(4)=7, a(5)=16, a(n)=4*a(n-1)- 2*a(n-2)- 6*a(n-3)+4*a(n-4)+2*a(n-5)-a(n-6). - _Harvey P. Dale_, Feb 02 2015
%F A032441 a(n) = A033192(n) + 1. - _Alois P. Heinz_, Jul 01 2018
%p A032441 a:= n-> (f-> f*(f+1)/2+1)((<<0|1>, <1|1>>^n)[1, 2]):
%p A032441 seq(a(n), n=0..35); # _Alois P. Heinz_, Jul 01 2018
%t A032441 Table[Sum[Binomial[Fibonacci[n],i],{i,0,2}],{n,0,30}] (* or *) LinearRecurrence[ {4,-2,-6,4,2,-1},{1,2,2,4,7,16},30] (* _Harvey P. Dale_, Feb 02 2015 *)
%Y A032441 Cf. A000045, A033192.
%K A032441 nonn
%O A032441 0,2
%A A032441 _N. J. A. Sloane_