A173151 a(n) = a(n-1) - [a(n-1)/2] + a(n-2) - [a(n-5)/2] where [k] = floor(k).

1, 1, 2, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 16, 17, 20, 21, 25, 26, 30, 31, 36, 37, 42, 43, 49, 50, 56, 57, 64, 65, 72, 73, 81, 82, 90, 91, 100, 101, 110, 111, 121, 122, 132, 133, 144, 145, 156, 157, 169, 170

Offset: 0

Author

Roger L. Bagula, Nov 22 2010

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Programs

Mathematica

f[-3] = 0; f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;
f[n_] := f[n] = f[n - 1] + f[n - 2] - Floor[f[n - 1]/2] - Floor[f[n - 5]/2]
Table[f[n], {n, 0, 50}]

Formula

a(n) = a(n-1)-floor[a(n-1)/2]+a(n-2)-floor[a(n-5)/2].

From Chai Wah Wu, Jun 02 2016: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) - a(n-6) + a(n-7) for n > 6.

G.f.: (-x^5 + x^4 - 1)/((x - 1)^3*(x + 1)^2*(x^2 + 1)). (End)

a(n) = ((-1)^n*(11 - 2*n) + 2*n*(n + 5) + 4*sin(Pi*n/2) - 4*cos(Pi*n/2) + 25)/32. - Ilya Gutkovskiy, Jun 03 2016