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Search: id:A106516
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| A106516 |
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A Pascal-like triangle based on 3^n. |
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+0
2
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| 1, 3, 1, 9, 4, 1, 27, 13, 5, 1, 81, 40, 18, 6, 1, 243, 121, 58, 24, 7, 1, 729, 364, 179, 82, 31, 8, 1, 2187, 1093, 543, 261, 113, 39, 9, 1, 6561, 3280, 1636, 804, 374, 152, 48, 10, 1, 19683, 9841, 4916, 2440, 1178, 526, 200, 58, 11, 1, 59049, 29524, 14757, 7356, 3618
(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 A027649. Diagonal sums are A106517.
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FORMULA
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Riordan array (1/(1-3x), x/(1-x)); Number triangle T(n, 0)=A000244(n), T(n, k)=T(n-1, k-1)+T(n-1, k); T(n, k)=sum{j=0..n, binomial(n, k+j)2^j}.
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EXAMPLE
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Triangle begins
1;
3,1;
9,4,1;
27,13,5,1;
81,40,18,6,1;
243,121,58,24,7,1;
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CROSSREFS
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Columns 1, 2, 3, 4, 5: A003462, A000340, A052150, A097786, A097787.
Sequence in context: A126186 A162852 A054448 this_sequence A140071 A067417 A016577
Adjacent sequences: A106513 A106514 A106515 this_sequence A106517 A106518 A106519
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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 05 2005
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