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Search: id:A108359
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| A108359 |
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A symmetric number triangle based on floor((n+2)/2). |
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+0
5
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| 1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 14, 7, 1, 1, 9, 28, 28, 9, 1, 1, 11, 47, 76, 47, 11, 1, 1, 13, 71, 163, 163, 71, 13, 1, 1, 15, 100, 301, 433, 301, 100, 15, 1, 1, 17, 134, 502, 961, 961, 502, 134, 17, 1, 1, 19, 173, 778, 1879, 2515, 1879, 778, 173, 19, 1, 1, 21, 217, 1141
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are A108360. Diagonal sums are A108361.
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FORMULA
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Number triangle T(n, k)=sum{j=0..n-k, C(k, j)C(n-j, k)*floor((j+2)/2)}. As a square array read by anti-diagonals, T(n, k)=sum{j=0..n, C(k, j)C(n+k-j, k)*floor((j+2)/2)}.
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EXAMPLE
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Rows begin
1;
1,1;
1,3,1;
1,5,5,1;
1,7,14,7,1;
1,9,28,28,9,1;
1,11,47,76,47,11,1
As a square array read by anti-diagonals, rows start
1,1,1,1,1,1,...
1,3,5,7,9,11,...
1,5,14,28,47,71,...
1,7,28,76,163,301,...
1,9,47,163,433,961,...
1,11,71,301,961,2515,...
1,13,100,502,1879,5695,...
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CROSSREFS
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Sequence in context: A008288 A144461 A106597 this_sequence A100936 A086620 A137897
Adjacent sequences: A108356 A108357 A108358 this_sequence A108360 A108361 A108362
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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), May 31 2005
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