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).

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

1,2

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.

Links

Table of n, a(n) for n=1..70.

Index entries for sequences related to the Josephus Problem

Formula

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

Example

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],...

Prog

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

Crossrefs

Cf. A100452, A100287, A000960, A101105.

Sequence in context: A269397 A267107 A126316 * A348366 A229120 A255067

Adjacent sequences: A101221 A101222 A101223 * A101225 A101226 A101227

Keyword

nonn,tabl

Author

Paul D. Hanna, Dec 01 2004

Status

approved