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%I #24 Mar 12 2024 12:54:56
%S 1,1,16,41,121,316,841,2201,5776,15121,39601,103676,271441,710641,
%T 1860496,4870841,12752041,33385276,87403801,228826121,599074576,
%U 1568397601,4106118241,10749957116,28143753121,73681302241,192900153616,505019158601,1322157322201
%N a(n) = -4 + 5*Fibonacci(n+1)^2.
%C a(1) and a(2n) are perfect squares.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-3,1).
%F a(n) = 3*a(n-1)-3*a(n-3)+a(n-4). G.f.: 1-x*(x^3-7*x^2+13*x+1) / ((x-1)*(x+1)*(x^2-3*x+1)). - _Colin Barker_, Sep 01 2013
%F a(n) = A005248(n+1) - A010696(n). - _R. J. Mathar_, Jan 18 2021
%t Table[-4 + 5*Fibonacci[n]^2, {n, 2, 31}] (* _Alonso del Arte_, Nov 17 2011 *)
%o (PARI) Vec(-x*(x^3-7*x^2+13*x+1)/((x-1)*(x+1)*(x^2-3*x+1)) + O(x^100)) \\ _Colin Barker_, Sep 01 2013
%Y Cf. A005248.
%K nonn,easy
%O 0,3
%A _Artur Jasinski_, Nov 17 2011
%E a(0)=1 prepended by _Alois P. Heinz_, Mar 11 2024
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