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Search: id:A104709
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| A104709 |
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Triangle read by rows: T(n,k)=sum{j=0..n, 2^(n-j)*binomial(j,k)}; Riordan array (1/((1-x)(1-2x)),x/(1-x)). |
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3
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| 1, 3, 1, 7, 4, 1, 15, 11, 5, 1, 31, 26, 16, 6, 1, 63, 57, 42, 22, 7, 1, 127, 120, 99, 64, 29, 8, 1, 255, 247, 219, 163, 93, 37, 9, 1, 511, 502, 466, 382, 256, 130, 46, 10, 1, 1023, 1013, 968, 848, 638, 386, 176, 56, 11, 1, 2047, 2036, 1981, 1816, 1486, 1024, 562, 232, 67
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums = A001787: 1, 4, 12, 32, 80, 192...(number of edges in n-dimensional hypercube).
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FORMULA
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Begin with A055248 as a triangle, delete leftmost column.
Factors as (1/(1-2x), x)*(1/(1-x), x/(1-x)) - the sequence array for 2^n times Pascal's triangle. - Paul Barry (pbarry(AT)wit.ie), Aug 05 2005
T(n, k)=sum{j=0..n-k, C(n-j, k)2^j}; - Paul Barry (pbarry(AT)wit.ie), Jan 12 2006
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EXAMPLE
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The first few rows are:
1;
3, 1;
7, 4, 1;
15, 11, 5, 1;
31, 26, 16, 6, 1;
63, 57, 42, 22, 7, 1;
...
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CROSSREFS
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Cf. A001787, A055248, A007318.
Sequence in context: A095868 A013602 A086272 this_sequence A110814 A021319 A010603
Adjacent sequences: A104706 A104707 A104708 this_sequence A104710 A104711 A104712
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 19 2005
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