|
%I #13 Jul 01 2018 19:25:15
%S 1,2,2,4,7,16,37,92,232,596,1541,4006,10441,27262,71254,186356,487579,
%T 1276004,3339821,8742472,22885996,59912932,156848617,410626154,
%U 1075018897,2814412826,7368190922,19290113572,50502074767,132215989336,346145696821,906220783316
%N a(n) = Sum_{i=0..2} binomial(Fibonacci(n),i).
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-6,4,2,-1).
%F 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 a(n) = A033192(n) + 1. - _Alois P. Heinz_, Jul 01 2018
%p a:= n-> (f-> f*(f+1)/2+1)((<<0|1>, <1|1>>^n)[1, 2]):
%p seq(a(n), n=0..35); # _Alois P. Heinz_, Jul 01 2018
%t 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 Cf. A000045, A033192.
%K nonn
%O 0,2
%A _N. J. A. Sloane_.
|
