A173692 a(n) = ceiling(A000931(n)/2).

0, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 11, 14, 19, 25, 33, 43, 57, 76, 100, 133, 176, 233, 308, 408, 541, 716, 949, 1257, 1665, 2205, 2921, 3870, 5126, 6791, 8996, 11917, 15786, 20912, 27703, 36698, 48615, 64401, 85313, 113015, 149713, 198328, 262728, 348041, 461056

Offset: 0

Author

Roger L. Bagula, Nov 25 2010

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000931.

Programs

Mathematica

a[0] = 0; a[1] = 1; a[2] = 1;
a[n_] := a[n] = a[n - 2] + a[n - 3]
Table[a[n] - Floor[a[n]/2], {n, 0, 30}]

PARI

concat(0, Vec(x*(1 + x)*(1 - x^3 - x^7) / ((1 - x)*(1 - x^2 - x^3)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) + O(x^40))) \\ Colin Barker, Feb 26 2020

Formula

a(n) = A000931(n) - floor(A000931(n)/2).

a(n) = a(n-2) + a(n-3) + a(n-7) - a(n-9) - a(n-10). - R. J. Mathar, Mar 11 2012

G.f.: x*(1 + x)*(1 - x^3 - x^7) / ((1 - x)*(1 - x^2 - x^3)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Colin Barker, Feb 26 2020

Extensions

More terms from Jinyuan Wang, Feb 26 2020