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a(n) = ceiling(A000931(n)/2).
1

%I #17 Feb 26 2020 10:06:26

%S 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,

%T 308,408,541,716,949,1257,1665,2205,2921,3870,5126,6791,8996,11917,

%U 15786,20912,27703,36698,48615,64401,85313,113015,149713,198328,262728,348041,461056

%N a(n) = ceiling(A000931(n)/2).

%H Colin Barker, <a href="/A173692/b173692.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,0,0,1,0,-1,-1).

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

%F a(n) = a(n-2) + a(n-3) + a(n-7) - a(n-9) - a(n-10). - _R. J. Mathar_, Mar 11 2012

%F 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

%t a[0] = 0; a[1] = 1; a[2] = 1;

%t a[n_] := a[n] = a[n - 2] + a[n - 3]

%t Table[a[n] - Floor[a[n]/2], {n, 0, 30}]

%o (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

%Y Cf. A000931.

%K nonn,easy

%O 0,7

%A _Roger L. Bagula_, Nov 25 2010

%E More terms from _Jinyuan Wang_, Feb 26 2020