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Search: id:A101224
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| A101224 |
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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). |
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+0
3
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| 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
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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FORMULA
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T(n, n) = A100287(n).
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EXAMPLE
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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],...
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PROGRAM
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(PARI) T(n, k)=if(k==1, n^2-n+1, (n-k+1)*floor((T(n, k-1)-1)/(n-k+1)))
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CROSSREFS
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Cf. A100452, A100287, A000960, A101105.
Adjacent sequences: A101221 A101222 A101223 this_sequence A101225 A101226 A101227
Sequence in context: A071574 A054429 A126316 this_sequence A139285 A080398 A082321
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Dec 01 2004
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