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A022403 a(0)=a(1)=3; thereafter a(n) = a(n-1) + a(n-2) + 1.

%I A022403 #29 Sep 08 2022 08:44:46
%S A022403 3,3,7,11,19,31,51,83,135,219,355,575,931,1507,2439,3947,6387,10335,
%T A022403 16723,27059,43783,70843,114627,185471,300099,485571,785671,1271243,
%U A022403 2056915,3328159,5385075,8713235,14098311,22811547,36909859,59721407,96631267,156352675,252983943,409336619,662320563
%N A022403 a(0)=a(1)=3; thereafter a(n) = a(n-1) + a(n-2) + 1.
%H A022403 G. C. Greubel, <a href="/A022403/b022403.txt">Table of n, a(n) for n = 0..1000</a>
%H A022403 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1)
%F A022403 From _R. J. Mathar_, Mar 11 2011:  (Start)
%F A022403 a(n+1) - a(n) = A022087(n).
%F A022403 G.f.: ( 3-3*x+x^2 ) / ( (x-1)*(x^2+x-1) ). (End)
%F A022403 a(n) = 4*Fibonacci(n+1) - 1. - _G. C. Greubel_, Mar 01 2018
%F A022403 a(n) = (-1 + (2^(1-n)*(-(1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n))) / sqrt(5)). - _Colin Barker_, Mar 02 2018
%t A022403 Table[4*Fibonacci[n+1] -1,{n, 0, 31}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 03 2011 *)
%t A022403 RecurrenceTable[{a[0]==a[1]==3,a[n]==a[n-1]+a[n-2]+1},a,{n,40}] (* or *) LinearRecurrence[{2,0,-1},{3,3,7},50] (* _Harvey P. Dale_, Jan 10 2021 *)
%o A022403 (PARI) for(n=0, 40, print1(4*fibonacci(n+1) -1, ", ")) \\ _G. C. Greubel_, Mar 01 2018
%o A022403 (Magma) [4*Fibonacci(n+1) - 1: n in [0..40]]; // _G. C. Greubel_, Mar 01 2018
%Y A022403 See A022406 for a similar sequence.
%K A022403 nonn
%O A022403 0,1
%A A022403 _N. J. A. Sloane_
%E A022403 Terms a(32) onward added by _G. C. Greubel_, Mar 01 2018