A121505 - OEIS

%I #12 Aug 29 2019 08:48:21

%S 1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,1,0,0,0,0,0,0,0

%N Hit triangle for unit circle area (Pi) approximation problem described in A121500.

%C Record for n=3,4,... only those (n, A121500(n)) pairs which have relative error E(n, A121500(n)) smaller than all errors with smaller n. This produces the table a(n,m).

%C The unit circle area is approximated by the arithmetic mean of the areas of an inscribed regular n-gon and a circumscribed regular m-gon.

%C For each row n>=3 the minimal relative error E(n,m):= ((Fin(n) + Fout(m))/2-Pi)/ Pi) appears for m= A121500(n).

%C The same hit triangle is obtained when one considers the minimal relative errors for the columns m>=3 and collects the sequence with decreasing errors, starting with m=3.

%H W. Lang: <a href="/A121505/a121505.txt">First rows.</a>

%F a(n,m) = 1 if m = A121500(n) and E(n,m) < min(E(k,A121500(k)), k=3..n-1), n>=4. a(3,3) = 1, else a(n,m) = 0.

%e [1], [0,0], [0,1,0], [0, 0, 1, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0],...

%K nonn,tabl,easy

%O 3,1

%A _Wolfdieter Lang_, Aug 16 2006