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a(0)=1, a(1)=4, a(n) = a(n-1) + a(n-2) - 1.
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%I #28 Apr 11 2024 10:11:08

%S 1,4,4,7,10,16,25,40,64,103,166,268,433,700,1132,1831,2962,4792,7753,

%T 12544,20296,32839,53134,85972,139105,225076,364180,589255,953434,

%U 1542688,2496121,4038808,6534928,10573735,17108662,27682396,44791057,72473452,117264508

%N a(0)=1, a(1)=4, a(n) = a(n-1) + a(n-2) - 1.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).

%F G.f.: -x*(-1-2*x+4*x^2) / ( (x-1)*(x^2+x-1) ). - _R. J. Mathar_, Mar 15 2011

%F a(n) = 1+3*|A039834(n)| = 1+3*A000045(n). - _R. J. Mathar_, Mar 15 2011

%t Join[{a=1,b=4},Table[c=a+b-1;a=b;b=c,{n,100}]]

%t LinearRecurrence[{2,0,-1},{1,4,4},40] (* _Harvey P. Dale_, Jun 06 2020 *)

%o (PARI) a(n)=3*fibonacci(n)+1 \\ _Charles R Greathouse IV_, Oct 29 2016

%Y Cf. A000045, A000071, A001611, A001612, A039834, A187890.

%K nonn,easy

%O 0,2

%A _Vladimir Joseph Stephan Orlovsky_, Mar 15 2011