A173894 a(n) = ceiling(A029826(n)/2).

1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 7, 8, 10, 11, 14, 16, 19, 22, 25, 31, 35, 42, 49, 58, 68, 80, 94, 110, 130, 152, 180, 210, 248, 292, 343, 404, 474, 558, 656, 772, 908, 1068, 1256, 1478, 1738, 2045, 2406, 2829, 3328, 3914, 4605, 5416, 6371, 7494, 8815, 10369, 12197, 14347

Offset: 0

Author

Roger L. Bagula, Nov 26 2010

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,0,1,1,1,1,1,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,-1,-1,-1,-1,-1,0,1,1).

Crossrefs

Cf. A029826.

Programs

Magma

R:= PowerSeriesRing(Integers(), 105);
A029826:= Coefficients(R!( 1/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10) ));
A173894:= func< n | Ceiling( A029826[n+1]/2 ) >;
[A173894(n): n in [0..100]]; // G. C. Greubel, Apr 23 2021

Mathematica

A029826 = CoefficientList[Series[1/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10), {x, 0, 250}], x];
Table[Ceiling[A029826[[n+1]]/2], {n, 0, 100}] (* modified by G. C. Greubel, Apr 23 2021 *)

Sage

A029826=[( 1/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10) ).series(x,n+1).list()[n] for n in (0..100)]
def A173894(n): return ceil( A029826[n]/2 )
[A173894(n) for n in (0..100)] # G. C. Greubel, Apr 23 2021

Formula

a(n) = ceiling(A029826(n)/2) = A029826(n) - floor(A029826(n)/2).