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

1,2

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).

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.

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 *)

Prog

(PARI) a(n)=if(n<1, 0, 1+(n\2)-(n\3))
(Magma) [1+Floor(n/2)-Floor(n/3): n in [1..90]]; // G. C. Greubel, Nov 09 2019
(Sage) [1+floor(n/2)-floor(n/3) for n in (1..40)] # G. C. Greubel, Nov 09 2019
(GAP) List([1..90], n-> 1+Int(n/2)-Int(n/3) ); # G. C. Greubel, Nov 09 2019

Crossrefs

Cf. A008615.

Sequence in context: A187035 A008615 A103221 * A261348 A320536 A347698

Adjacent sequences: A026803 A026804 A026805 * A026807 A026808 A026809

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved