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A213967 a(n)=n for n<=3; thereafter a(n)=a(n-1)+a(n-2)+a(n-3)+1.

%I A213967 #25 Sep 08 2022 08:46:02
%S A213967 0,1,2,3,7,13,24,45,83,153,282,519,955,1757,3232,5945,10935,20113,
%T A213967 36994,68043,125151,230189,423384,778725,1432299,2634409,4845434,
%U A213967 8912143,16391987,30149565,55453696,101995249,187598511,345047457,634641218,1167287187
%N A213967 a(n)=n for n<=3; thereafter a(n)=a(n-1)+a(n-2)+a(n-3)+1.
%D A213967 Atanassov, K. T.; Atanassova, V.; Shannon, A. G.; Turner, J. C. New visual perspectives on Fibonacci numbers. With a foreword by A. F. Horadam. World Scientific Publishing Co., Inc., River Edge, NJ, 2002. xvi+313 pp. ISBN: 981-238-134-1 MR1932564 (2003h:11015). See p. 68.
%H A213967 Bruno Berselli, <a href="/A213967/b213967.txt">Table of n, a(n) for n = 0..1000</a>
%H A213967 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-1).
%F A213967 G.f.: x*(1-x^2+x^3)/(1-2*x+x^4). - _Bruno Berselli_, Jul 02 2012
%p A213967 f:=proc(n) option remember; if n <= 3 then n else f(n-1)+f(n-2)+f(n-3)+1; fi; end:
%p A213967 seq(f(n),n=0..60);
%t A213967 Join[{0}, LinearRecurrence[{2, 0, 0, -1}, {1, 2, 3, 7}, 40]] (* _Jean-François Alcover_, Feb 13 2018 *)
%t A213967 nxt[{a_,b_,c_}]:={b,c,a+b+c+1}; Join[{0},NestList[nxt,{1,2,3},40][[All,1]]] (* _Harvey P. Dale_, Sep 07 2020 *)
%o A213967 (Magma) [n le 3 select n else Self(n)+Self(n-1)+Self(n-2)+1: n in [0..35]]; // _Bruno Berselli_, Jul 02 2012
%o A213967 (Haskell)
%o A213967 a213967 n = a213967_list !! n
%o A213967 a213967_list = 0 : xs where
%o A213967                xs = 1 : 2 : 3 : map (+ 1)
%o A213967                     (zipWith3 (((+) .) . (+)) xs (tail xs) (drop 2 xs))
%o A213967 -- _Reinhard Zumkeller_, Dec 29 2014
%Y A213967 Cf. A001590.
%Y A213967 Cf. A248098.
%K A213967 nonn,easy
%O A213967 0,3
%A A213967 _N. J. A. Sloane_, Jun 30 2012