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%I #16 Mar 29 2024 14:05:45
%S 1,6,8,15,24,40,65,106,172,279,452,732,1185,1918,3104,5023,8128,13152,
%T 21281,34434,55716,90151,145868,236020,381889,617910,999800,1617711,
%U 2617512,4235224,6852737,11087962
%N a(n) = a(n-1) + a(n-2) + 1, with a(0) = 1 and a(1) = 6.
%H G. C. Greubel, <a href="/A022320/b022320.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).
%F From _R. J. Mathar_, Apr 07 2011: (Start)
%F G.f.: (1 +4*x -4*x^2)/( (1-x)*(1-x-x^2) ).
%F a(n) = A022113(n) - 1. (End)
%F a(n) = 2*F(n+2) + 3*F(n) - 1, where F = A000045. - _G. C. Greubel_, Aug 25 2017
%t LinearRecurrence[{2,0,-1}, {1,6,8}, 50] (* _G. C. Greubel_, Aug 25 2017 *)
%t nxt[{a_,b_}]:={b,a+b+1}; NestList[nxt,{1,6},40][[;;,1]] (* _Harvey P. Dale_, Mar 29 2024 *)
%o (PARI) x='x+O('x^50); Vec((1 +4*x -4*x^2)/((1-x)*(1-x-x^2))) \\ _G. C. Greubel_, Aug 25 2017
%Y Cf. A000045.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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