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Search: id:A110537
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| A110537 |
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Symmetric number square associated to ceiling(k^n/n^k), read by antidiagonals. |
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+0
4
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| 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 3, 4, 4, 3, 1, 1, 3, 5, 7, 5, 3, 1, 1, 4, 7, 9, 9, 7, 4, 1, 1, 5, 11, 15, 14, 15, 11, 5, 1, 1, 8, 18, 25, 24, 24, 25, 18, 8, 1, 1, 12, 35, 47, 40, 47, 40, 47, 35, 12, 1, 1, 18, 72, 102, 79, 81, 81, 79, 102, 72, 18, 1, 1, 30, 152, 237, 183, 168
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums of triangle are A110538. Diagonal sums are A110539. The row sums of the inverse of the triangle may be A000007.
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FORMULA
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Number square T(n, k)=sum{j=1..min(n, k), ceiling(j^n/n^j)*ceiling(j^k/k^j)}; As a number triangle, T(n, k)=if(k<=n, sum{j=1..min(n-k+1, k), ceiling(j^(n-k+1)/(n-k+1)^j)*ceiling(j^k/k^j)}, 0)
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EXAMPLE
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As a number square, rows begin
1,1,1,1,1,1,1,...
1,2,2,2,3,3,4,...
1,2,3,4,5,7,11,...
1,2,4,7,9,15,25,...
1,3,5,9,14,24,40,...
1,3,7,15,24,47,81,...
As a number triangle, rows begin
1;
1,1;
1,2,1;
1,2,2,1;
1,2,3,2,1;
1,3,4,4,3,1;
1,3,5,7,5,3,1;
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CROSSREFS
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Sequence in context: A113453 A003983 A087062 this_sequence A138015 A103444 A099172
Adjacent sequences: A110534 A110535 A110536 this_sequence A110538 A110539 A110540
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jul 25 2005
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