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Search: id:A099233
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| A099233 |
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Square array read by anti-diagonals associated to sections of 1/(1-x-x^k). |
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+0
6
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| 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 6, 5, 1, 1, 1, 5, 10, 13, 8, 1, 1, 1, 6, 15, 26, 28, 13, 1, 1, 1, 7, 21, 45, 69, 60, 21, 1, 1, 1, 8, 28, 71, 140, 181, 129, 34, 1, 1, 1, 9, 36, 105, 251, 431, 476, 277, 55, 1, 1, 1, 10, 45, 148, 413, 882, 1326, 1252, 595, 89, 1
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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Sums of anti-diagonals are A099236. Main diagonal is A099237. Rows include A000045, A002478, A099234, A099235. Columns include A000217, A008778.
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FORMULA
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Square array T(n, k)=sum{j=0..n, binomial(k(n-j), j)}. Rows are generated by 1/(1-x(1+x)^k) and satisfy a(n)=sum{k=0..n, C(n, k)a(n-k-1)}.
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EXAMPLE
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Rows begin
1,1,1,1,1,1,...
1,1,2,3,5,8,...
1,1,3,6,13,28,...
1,1,4,10,26,69,...
1,1,5,15,45,140...
Row 1 is the 0-section of 1/(1-x-x) (A000079)
Row 2 is the 1-section of 1/(1-x-x^2) (A000045)
Row 3 is the 2-section of 1/(1-x-x^3) (A000930)
Row 4 is the 3-section of 1/(1-x-x^4) (A003269)
etc
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CROSSREFS
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Cf. A099238.
Adjacent sequences: A099230 A099231 A099232 this_sequence A099234 A099235 A099236
Sequence in context: A047030 A047120 A096751 this_sequence A133815 A130580 A110541
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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), Oct 08 2004
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