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%I #21 Apr 24 2021 03:33:37
%S 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,
%T 16,19,22,25,31,35,42,49,58,68,80,94,110,130,152,180,210,248,292,343,
%U 404,474,558,656,772,908,1068,1256,1478,1738,2045,2406,2829,3328,3914,4605,5416,6371,7494,8815,10369,12197,14347
%N a(n) = ceiling(A029826(n)/2).
%H G. C. Greubel, <a href="/A173894/b173894.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_41">Index entries for linear recurrences with constant coefficients</a>, 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).
%F a(n) = ceiling(A029826(n)/2) = A029826(n) - floor(A029826(n)/2).
%t A029826 = CoefficientList[Series[1/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10), {x, 0, 250}], x];
%t Table[Ceiling[A029826[[n+1]]/2], {n, 0, 100}] (* modified by _G. C. Greubel_, Apr 23 2021 *)
%o (Magma)
%o R<x>:= PowerSeriesRing(Integers(), 105);
%o A029826:= Coefficients(R!( 1/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10) ));
%o A173894:= func< n | Ceiling( A029826[n+1]/2 ) >;
%o [A173894(n): n in [0..100]]; // _G. C. Greubel_, Apr 23 2021
%o (Sage)
%o 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)]
%o def A173894(n): return ceil( A029826[n]/2 )
%o [A173894(n) for n in (0..100)] # _G. C. Greubel_, Apr 23 2021
%Y Cf. A029826.
%K nonn,easy
%O 0,17
%A _Roger L. Bagula_, Nov 26 2010
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