A100463 a(n) = 2^(n-1) - A100462(n).

0, 1, 3, 5, 9, 7, 15, 19, 27, 31, 21, 29, 45, 49, 75, 85, 97, 65, 63, 101, 153, 125, 157, 127, 177, 163, 165, 199, 229, 199, 217, 277, 253, 325, 315, 365, 345, 379, 423, 449, 549, 529, 597, 409, 507, 473, 633, 569, 717, 523, 651, 655, 777, 793, 825, 835, 855, 833

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Maple

A100461:= proc(m, n) option remember;
   if m=1 then 2^(n-1);
   else (n-m+1)*floor((A100461(m-1, n)-1)/(n-m+1));
fi; end:
A100462:= proc(n) A100461(n, n); end:
A100463:= proc(n) 2^(n-1) - A100462(n); end:
seq(A100463(n), n=1..100); # R. J. Mathar, Aug 06 2007

Mathematica

t[n_, k_]:= t[n, k]= If[k==1, 2^(n-1), If[k<n+1, (n-k+1)*Floor[(t[n, k -1] -1)/(n-k+1)], 0]]; (* t = A100461 *)
Table[2^(n-1) -t[n, n], {n, 60}] (* G. C. Greubel, Apr 07 2023 *)

Prog

(Magma)
function t(n, k) // t = A100461
  if k eq 1 then return 2^(n-1);
  else return (n-k+1)*Floor((t(n, k-1) -1)/(n-k+1));
  end if;
end function;
[2^(n-1) - t(n, n): n in [1..60]]; // G. C. Greubel, Apr 07 2023
(SageMath)
def t(n, k): # t = A100461
    if (k==1): return 2^(n-1)
    else: return (n-k+1)*((t(n, k-1) -1)//(n-k+1))
[2^(n-1) - t(n, n) for n in range(1, 61)] # G. C. Greubel, Apr 07 2023

Crossrefs

Cf. A100461, A100462.

Sequence in context: A003961 A332818 A348437 * A346969 A166722 A094549

Adjacent sequences: A100460 A100461 A100462 * A100464 A100465 A100466

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 23 2004

Extensions

More terms from R. J. Mathar, Aug 06 2007

Status

approved