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A101224 Triangle, read by rows, where T(n,1) = n^2-n+1 for n>=1 and T(n,k) = (n-k+1)*floor( (T(n,k-1)-1)/(n-k+1) ) for 1 related to the Flavius sieve (A000960).

%I A101224 #9 Jun 23 2020 19:05:23
%S A101224 1,3,2,7,6,5,13,12,10,9,21,20,18,16,15,31,30,28,27,26,25,43,42,40,36,
%T A101224 33,32,31,57,56,54,50,48,45,44,43,73,72,70,66,65,64,63,62,61,91,90,88,
%U A101224 84,78,75,72,69,68,67,111,110,108,104,98,96,95,92,90,88,87,133,132,130,126
%N A101224 Triangle, read by rows, where T(n,1) = n^2-n+1 for n>=1 and T(n,k) = (n-k+1)*floor( (T(n,k-1)-1)/(n-k+1) ) for 1<k<=n; related to the Flavius sieve (A000960).
%C A101224 A variant of triangle A100452. The main diagonal equals A100287, the first number that is crossed off at stage n in the Flavius sieve (A000960). Row sums are A101105.
%H A101224 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%F A101224 T(n, n) = A100287(n).
%e A101224 T(4,4) = 9 since we start with T(4,1)=4^2-4+1=13 and then
%e A101224 T(4,2)=(4-2+1)*floor((T(4,1)-1)/(4-2+1))=3*floor((13-1)/3)=12,
%e A101224 T(4,3)=(4-3+1)*floor((T(4,2)-1)/(4-3+1))=2*floor((12-1)/2)=10,
%e A101224 T(4,4)=(4-4+1)*floor((T(4,3)-1)/(4-4+1))=1*floor((10-1)/1)=9.
%e A101224 Rows begin:
%e A101224 [1],
%e A101224 [3,2],
%e A101224 [7,6,5],
%e A101224 [13,12,10,9],
%e A101224 [21,20,18,16,15],
%e A101224 [31,30,28,27,26,25],
%e A101224 [43,42,40,36,33,32,31],
%e A101224 [57,56,54,50,48,45,44,43],
%e A101224 [73,72,70,66,65,64,63,62,61],...
%o A101224 (PARI) T(n,k)=if(k==1,n^2-n+1,(n-k+1)*floor((T(n,k-1)-1)/(n-k+1)))
%Y A101224 Cf. A100452, A100287, A000960, A101105.
%K A101224 nonn,tabl
%O A101224 1,2
%A A101224 _Paul D. Hanna_, Dec 01 2004