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A242774 a(n) = ceiling( n / 2 ) + ceiling( n / 3 ).

%I A242774 #33 Sep 08 2022 08:46:08
%S A242774 2,2,3,4,5,5,7,7,8,9,10,10,12,12,13,14,15,15,17,17,18,19,20,20,22,22,
%T A242774 23,24,25,25,27,27,28,29,30,30,32,32,33,34,35,35,37,37,38,39,40,40,42,
%U A242774 42,43,44,45,45,47,47,48,49,50,50,52,52,53,54,55,55,57
%N A242774 a(n) = ceiling( n / 2 ) + ceiling( n / 3 ).
%H A242774 G. C. Greubel, <a href="/A242774/b242774.txt">Table of n, a(n) for n = 1..5000</a>
%H A242774 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,-1).
%H A242774 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%F A242774 G.f.: x * (2 + 2*x + x^2) / (1 - x^2 - x^3 + x^5) = (2*x + 2*x^2 + x^3) / ((1 - x^2) * (1 - x^3)).
%F A242774 a(n) = - A010761(-n) = 2 - a(1-n). a(n) = A002789(n) - A002789(n-1) for all n in Z.
%F A242774 a(n) = Sum_{k=1..n} A000035(k) + A000035(A010872(k)). - _Benedict W. J. Irwin_, Apr 13 2016
%F A242774 E.g.f.: 5*x*exp(x)/6 - exp(-x)/4 + 7*exp(x)/12 + sin(sqrt(3)*x/2)*exp(-x/2)/(3*sqrt(3)) - cos(sqrt(3)*x/2)*exp(-x/2)/3. - _Ilya Gutkovskiy_, Apr 13 2016
%e A242774 G.f. = 2*x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 5*x^6 + 7*x^7 + 7*x^8 + ...
%p A242774 A242774:=n->ceil(n/2)+ceil(n/3): seq(A242774(n), n=1..100); # _Wesley Ivan Hurt_, Apr 13 2016
%t A242774 a[ n_] := Ceiling[ n / 2 ] + Ceiling[ n / 3 ];
%t A242774 LinearRecurrence[{0, 1, 1, 0, -1}, {2, 2, 3, 4, 5}, 100] (* _Vincenzo Librandi_, Apr 15 2016 *)
%t A242774 Rest[CoefficientList[Series[x*(2+2*x+x^2)/(1-x^2-x^3+x^5), {x, 0, 50}], x]] (* _G. C. Greubel_, Aug 06 2018 *)
%o A242774 (PARI) {a(n) = ceil( n / 2 ) + ceil( n / 3 )};
%o A242774 (PARI) {a(n) = if( n<0, polcoeff( -(x^2 + 2*x^3 + 2*x^4) / ((1 - x^2) * (1 - x^3)) + x * O(x^-n), -n), polcoeff( (2*x + 2*x^2 + x^3) / ((1 - x^2) * (1 - x^3)) + x * O(x^n), n))};
%o A242774 (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(2+2*x+x^2)/(1-x^2-x^3+x^5)));  // _G. C. Greubel_, Aug 06 2018
%Y A242774 Cf. A002789, A010761, A110654.
%Y A242774 Cf. A000035, A010872.
%K A242774 nonn,easy
%O A242774 1,1
%A A242774 _Michael Somos_, May 22 2014