A173388 a(n) = a(n - 3) + a(n - 4) if n is even, else a(n - 2) + a(n - 3).

1, 1, 1, 1, 2, 2, 2, 4, 4, 6, 6, 10, 10, 16, 16, 26, 26, 42, 42, 68, 68, 110, 110, 178, 178, 288, 288, 466, 466, 754, 754, 1220, 1220, 1974, 1974, 3194, 3194, 5168, 5168, 8362, 8362, 13530, 13530, 21892, 21892, 35422, 35422, 57314, 57314, 92736, 92736

Offset: 0

Author

Roger L. Bagula, Feb 17 2010

Keywords

• nonn
• easy
• less

Comments

The sequence is designed so that all the numbers, see A055389 or A006355, except the first two appear twice.

The limiting ratio a(n+1)/a(n) alternates between the golden ratio and one.

Essentially the same as A214927 (except for the first 4 terms and the offset). - Georg Fischer, Oct 01 2018

Programs

Mathematica

a[0] = 1; a[1] = 1; a[2] = 1; a[3] = 1;
a[n_] := a[n] = If[Mod[n, 2] == 0, a[n - 3] + a[n - 4], a[n - 2] + a[n - 3]];
Table[a[n], {n, 0, 50}]

Formula

a(n) = a(n-2)+a(n-4), n > 7.

G.f.: (x^7+1+x-x^6)/(1-x^2-x^4).

Extensions

Formula added by the Assoc. Editors of the OEIS, Feb 24 2010