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

0, 1, 2, 3, 7, 13, 24, 45, 83, 153, 282, 519, 955, 1757, 3232, 5945, 10935, 20113, 36994, 68043, 125151, 230189, 423384, 778725, 1432299, 2634409, 4845434, 8912143, 16391987, 30149565, 55453696, 101995249, 187598511, 345047457, 634641218, 1167287187

Offset: 0

Author

N. J. A. Sloane, Jun 30 2012

Keywords

• nonn
• easy

References

• 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.

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,0,-1).

Crossrefs

Cf. A001590.

Cf. A248098.

Programs

Haskell

a213967 n = a213967_list !! n
a213967_list = 0 : xs where
               xs = 1 : 2 : 3 : map (+ 1)
                    (zipWith3 (((+) .) . (+)) xs (tail xs) (drop 2 xs))
-- Reinhard Zumkeller, Dec 29 2014

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

Maple

f:=proc(n) option remember; if n <= 3 then n else f(n-1)+f(n-2)+f(n-3)+1; fi; end:
seq(f(n),n=0..60);

Mathematica

Join[{0}, LinearRecurrence[{2, 0, 0, -1}, {1, 2, 3, 7}, 40]] (* Jean-François Alcover, Feb 13 2018 *)
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 *)

Formula

G.f.: x*(1-x^2+x^3)/(1-2*x+x^4). - Bruno Berselli, Jul 02 2012