|
%I #16 Mar 06 2023 02:59:05
%S 1,2,1,2,2,2,2,3,2,3,3,3,3,4,3,4,4,4,4,5,4,5,5,5,5,6,5,6,6,6,6,7,6,7,
%T 7,7,7,8,7,8,8,8,8,9,8,9,9,9,9,10,9,10,10,10,10,11,10,11,11,11,11,12,
%U 11,12,12,12,12,13,12,13,13,13,13,14,13,14,14,14,14,15,14,15,15,15,15
%N a(n) = number of numbers k such that only one partition of n has least part k.
%H G. C. Greubel, <a href="/A026806/b026806.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,-1).
%F G.f.: x*(1+2*x-x^3-x^4)/((1-x^2)*(1-x^3)).
%F a(n) = A008615(n+6) = 1 + A008615(n), n>0.
%p seq(1+floor(n/2)-floor(n/3), n = 0..90); # _G. C. Greubel_, Nov 09 2019
%t Rest[CoefficientList[Series[x(1+2x-x^3-x^4)/((1-x^2)(1-x^3)), {x,0,90}], x]] (* _Harvey P. Dale_, Apr 22 2011 *)
%t Table[1 + Floor[n/2] - Floor[n/3], {n, 90}] (* _G. C. Greubel_, Nov 09 2019 *)
%o (PARI) a(n)=if(n<1,0,1+(n\2)-(n\3))
%o (Magma) [1+Floor(n/2)-Floor(n/3): n in [1..90]]; // _G. C. Greubel_, Nov 09 2019
%o (Sage) [1+floor(n/2)-floor(n/3) for n in (1..40)] # _G. C. Greubel_, Nov 09 2019
%o (GAP) List([1..90], n-> 1+Int(n/2)-Int(n/3) ); # _G. C. Greubel_, Nov 09 2019
%Y Cf. A008615.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_
|
