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Search: id:A115216
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| A115216 |
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"Correlation triangle" for 2^n. |
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+0
1
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| 1, 2, 2, 4, 5, 4, 8, 10, 10, 8, 16, 20, 21, 20, 16, 32, 40, 42, 42, 40, 32, 64, 80, 84, 85, 84, 80, 64, 128, 160, 168, 170, 170, 168, 160, 128, 256, 320, 336, 340, 341, 340, 336, 320, 256, 512, 640, 672, 680, 682, 682, 680, 672, 640, 512, 1024, 1280, 1344, 1360, 1364
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums are A102301. T(2n,n) gives A002450(n+1). Diagonal sums are A115217. Construction: Take antidiagonal triangle of MM^T where M is the sequence array for the sequence 2^n.
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FORMULA
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Number triangle T(n, k)=sum{j=0..n, [j<=k]*2^(k-j)[j<=n-k]*2^(n-k-j)}.
G.f.: 1/((1-2*x)*(1-2*x*y)*(1-x^2*y)) (Christian G. Bower (bowerc(AT)usa.net), Jan 17 2006)
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EXAMPLE
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Triangle begins
1,
2, 2,
4, 5, 4,
8, 10, 10, 8,
16, 20, 21, 20, 16,
32, 40, 42, 42, 40, 32,
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CROSSREFS
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Cf. A003983.
Sequence in context: A128900 A136099 A072454 this_sequence A122543 A118003 A159296
Adjacent sequences: A115213 A115214 A115215 this_sequence A115217 A115218 A115219
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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), Jan 16 2006
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