%I #16 Sep 29 2019 10:31:41
%S 1,1,1,3,7,21,57,157,421,1123,2971,7833,20593,54057,141753,371491,
%T 973183,2548813,6674473,17476581,45758461,119803971,313661811,
%U 821194993,2149945057,5628675601,14736139057,38579834307,101003513911,264430950213,692289729561
%N a(n) = Fibonacci(n)^2 - Fibonacci(n) + 1.
%C Subsequence of A002061.
%H Harvey P. Dale, <a href="/A262184/b262184.txt">Table of n, a(n) for n = 0..1000</a>
%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(n) = A000045(n)^2 - A000045(n) + 1.
%F G.f.: -(x^5+x^4-7*x^3+x^2+3*x-1) / ((x-1)*(x+1)*(x^2-3*x+1)*(x^2+x-1)). - _Alois P. Heinz_, Sep 15 2015
%e For n=2, a(n) = Fibonacci(n)^2 - Fibonacci(n) + 1 = 1^2 - 1 + 1 = 1.
%t #^2-#+1&/@Fibonacci[Range[0,30]] (* or *) LinearRecurrence[{4,-2,-6,4,2,-1},{1,1,1,3,7,21},40] (* _Harvey P. Dale_, Sep 29 2019 *)
%o (PARI) a(n) = fibonacci(n)^2 - fibonacci(n) + 1;
%o vector(30,n,a(n))
%Y Cf. A000045, A002061.
%K nonn,easy
%O 0,4
%A _Altug Alkan_, Sep 14 2015