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

%I A100463 #12 Apr 07 2023 09:26:35
%S A100463 0,1,3,5,9,7,15,19,27,31,21,29,45,49,75,85,97,65,63,101,153,125,157,
%T A100463 127,177,163,165,199,229,199,217,277,253,325,315,365,345,379,423,449,
%U A100463 549,529,597,409,507,473,633,569,717,523,651,655,777,793,825,835,855,833
%N A100463 a(n) = 2^(n-1) - A100462(n).
%H A100463 G. C. Greubel, <a href="/A100463/b100463.txt">Table of n, a(n) for n = 1..1000</a>
%p A100463 A100461:= proc(m,n) option remember;
%p A100463    if m=1 then 2^(n-1);
%p A100463    else (n-m+1)*floor((A100461(m-1,n)-1)/(n-m+1));
%p A100463 fi; end:
%p A100463 A100462:= proc(n) A100461(n,n); end:
%p A100463 A100463:= proc(n) 2^(n-1) - A100462(n); end:
%p A100463 seq(A100463(n), n=1..100); # _R. J. Mathar_, Aug 06 2007
%t A100463 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 *)
%t A100463 Table[2^(n-1) -t[n,n], {n,60}] (* _G. C. Greubel_, Apr 07 2023 *)
%o A100463 (Magma)
%o A100463 function t(n,k) // t = A100461
%o A100463   if k eq 1 then return 2^(n-1);
%o A100463   else return (n-k+1)*Floor((t(n,k-1) -1)/(n-k+1));
%o A100463   end if;
%o A100463 end function;
%o A100463 [2^(n-1) - t(n,n): n in [1..60]]; // _G. C. Greubel_, Apr 07 2023
%o A100463 (SageMath)
%o A100463 def t(n, k): # t = A100461
%o A100463     if (k==1): return 2^(n-1)
%o A100463     else: return (n-k+1)*((t(n, k-1) -1)//(n-k+1))
%o A100463 [2^(n-1) - t(n, n) for n in range(1, 61)] # _G. C. Greubel_, Apr 07 2023
%Y A100463 Cf. A100461, A100462.
%K A100463 nonn,easy
%O A100463 1,3
%A A100463 _N. J. A. Sloane_, Nov 23 2004
%E A100463 More terms from _R. J. Mathar_, Aug 06 2007