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Search: id:A111049
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| A111049 |
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Triangle T(n,k), 0<=k<=n, read by rows, given by [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,0, ...] where DELTA is the operator defined in A084938. |
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+0
1
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| 1, 1, 1, 1, 3, 2, 1, 6, 9, 4, 1, 11, 27, 25, 8, 1, 20, 70, 100, 65, 16, 1, 37, 170, 330, 325, 161, 32, 1, 70, 399, 980, 1295, 966, 385, 64, 1, 135, 917, 2723, 4515, 4501, 2635, 2695, 897, 128, 1, 264, 2076, 7224, 14406, 17976, 14364, 7176, 2049
(list; table; graph; listen)
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OFFSET
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0,5
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FORMULA
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T(n, k) = 2^(n-1)binomial(n-1, k-1)+binomial(n-1, k).
Sum_{k, 0<=k<=n} T(n, k) = 2^(n-1)*(1+2^(n-1)) = A063376(n-1) for n>=1.
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EXAMPLE
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Rows begin:
1;
1, 1;
1, 3, 2;
1, 6, 9, 4;
1, 11, 27, 25, 8;
1, 20, 70, 100, 65, 16;
1, 37, 170, 330, 325, 161, 32;
1, 70, 399, 980, 1295, 966, 385, 64;
1, 135, 917, 2723, 4515, 4501, 2695, 897, 128;
1, 264, 2076, 7224, 14406, 17976, 14364, 7176, 2049, 256;
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CROSSREFS
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Cf. A002064, A006127.
Sequence in context: A132276 A114586 A052174 this_sequence A088617 A008276 A094638
Adjacent sequences: A111046 A111047 A111048 this_sequence A111050 A111051 A111052
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 07 2005
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