A026806 a(n) = number of numbers k such that only one partition of n has least part k.

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, 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, 11, 12, 12, 12, 12, 13, 12, 13, 13, 13, 13, 14, 13, 14, 14, 14, 14, 15, 14, 15, 15, 15, 15

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A008615.

Programs

GAP

List([1..90], n-> 1+Int(n/2)-Int(n/3) ); # G. C. Greubel, Nov 09 2019

Magma

[1+Floor(n/2)-Floor(n/3): n in [1..90]]; // G. C. Greubel, Nov 09 2019

Maple

seq(1+floor(n/2)-floor(n/3), n = 0..90); # G. C. Greubel, Nov 09 2019

Mathematica

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 *)
Table[1 + Floor[n/2] - Floor[n/3], {n, 90}] (* G. C. Greubel, Nov 09 2019 *)

PARI

a(n)=if(n<1,0,1+(n\2)-(n\3))

Sage

[1+floor(n/2)-floor(n/3) for n in (1..40)] # G. C. Greubel, Nov 09 2019

Formula

G.f.: x*(1+2*x-x^3-x^4)/((1-x^2)*(1-x^3)).

a(n) = A008615(n+6) = 1 + A008615(n), n>0.