A173276 a(n) = a(n-2) + a(n-3) - floor(a(n-3)/2) - floor(a(n-4)/2).

1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28

Offset: 0

Author

Roger L. Bagula, Nov 22 2010

Keywords

• nonn
• easy

Comments

Instead of the Fibonacci sequence this has the base Padovan sequence.

The a(n+1)/a(n) ratio approaches one.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Crossrefs

Cf. A000931 (Padovan), A085269.

Programs

Magma

[Floor((2*n+5)/5) : n in [0..50]]; // Wesley Ivan Hurt, Mar 15 2015

Maple

A173276:=n->floor((2*n+5)/5): seq(A173276(n), n=0..50); # Wesley Ivan Hurt, Mar 15 2015

Mathematica

f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;
f[n_] := f[n] = f[n - 2] + f[n - 3] - Floor[f[n - 3]/2] - Floor[f[n - 4]/2]
Table[f[n], {n, 0, 50}]
nxt[{a_,b_,c_,d_}]:={b,c,d,c+b-Floor[b/2]-Floor[a/2]}; NestList[nxt,{1,1,1,2},70][[;;,1]] (* Harvey P. Dale, Jul 30 2023 *)

PARI

vector(100,n,(2*n+3)\5) \\ Derek Orr, Mar 21 2015

Formula

a(n) = a(n-2)+a(n-3)-floor(a(n-3)/2)-floor(a(n-4)/2).

Empirical g.f.: (x^3+1) / (x^6-x^5-x+1) = (x+1)*(x^2-x+1) / ((x-1)^2*(x^4+x^3+x^2+x+1)). - Colin Barker, Mar 23 2013

From Wesley Ivan Hurt, Mar 15 2015: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6).

a(n) = floor( (2n+5)/5 ). (End)