OFFSET

1,1

COMMENTS

See A186350 for a discussion of adjusted joint rank sequences.

EXAMPLE

MATHEMATICA

(* adjusted joint rank sequences a and b, using general formula for ranking 1st degree u*n+v and 2nd degree x*n^2+y*n+z *)

d=-1/2; u=6; v=0; x=1/2; y=1/2; (* 6i and triangular *)

h[n_]:=(-y+(4x(u*n+v-d)+y^2)^(1/2))/(2x);

a[n_]:=n+Floor[h[n]]; (* rank of u*n+v *)

k[n_]:=(x*n^2+y*n-v+d)/u;

b[n_]:=n+Floor[k[n]]; (* rank of x*n^2+y*n+d *)

Table[a[n], {n, 1, 120}] (* A186389 *)

Table[b[n], {n, 1, 100}] (* A186390 *)

CROSSREFS

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 19 2011

STATUS

approved