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 1A000960).

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, 33, 32, 31, 57, 56, 54, 50, 48, 45, 44, 43, 73, 72, 70, 66, 65, 64, 63, 62, 61, 91, 90, 88, 84, 78, 75, 72, 69, 68, 67, 111, 110, 108, 104, 98, 96, 95, 92, 90, 88, 87, 133, 132, 130, 126

Offset: 1

Author

Paul D. Hanna, Dec 01 2004

Keywords

• nonn
• tabl

Comments

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.

Examples

			T(4,4) = 9 since we start with T(4,1)=4^2-4+1=13 and then
T(4,2)=(4-2+1)*floor((T(4,1)-1)/(4-2+1))=3*floor((13-1)/3)=12,
T(4,3)=(4-3+1)*floor((T(4,2)-1)/(4-3+1))=2*floor((12-1)/2)=10,
T(4,4)=(4-4+1)*floor((T(4,3)-1)/(4-4+1))=1*floor((10-1)/1)=9.
Rows begin:
[1],
[3,2],
[7,6,5],
[13,12,10,9],
[21,20,18,16,15],
[31,30,28,27,26,25],
[43,42,40,36,33,32,31],
[57,56,54,50,48,45,44,43],
[73,72,70,66,65,64,63,62,61],...
		

Links

• Index entries for sequences related to the Josephus Problem

Crossrefs

Cf. A100452, A100287, A000960, A101105.

Programs

PARI

T(n,k)=if(k==1,n^2-n+1,(n-k+1)*floor((T(n,k-1)-1)/(n-k+1)))

Formula

T(n, n) = A100287(n).