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A071675
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Array read by antidiagonals of trinomial coefficients.
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9
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1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 0, 3, 3, 1, 0, 0, 2, 6, 4, 1, 0, 0, 1, 7, 10, 5, 1, 0, 0, 0, 6, 16, 15, 6, 1, 0, 0, 0, 3, 19, 30, 21, 7, 1, 0, 0, 0, 1, 16, 45, 50, 28, 8, 1, 0, 0, 0, 0, 10, 51, 90, 77, 36, 9, 1, 0, 0, 0, 0, 4, 45, 126, 161, 112, 45, 10, 1, 0, 0, 0, 0, 1, 30, 141, 266, 266
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| Read as a number triangle, this is the Riordan array (1, x(1+x+x^2)) with T(n,k)=sum{i=0..floor((n+k)/2), C(k,2i+2k-n)C(2i+2k-n,i)}. Rows start {1}, {0,1}, {0,1,1}, {0,1,2,1}, {0,0,3,3,1},... Row sums are then the trinomial numbers A000073(n+2). Diagonal sums are A013979. - Paul Barry (pbarry(AT)wit.ie), Feb 15 2005
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FORMULA
| T(n, k) =T(n-1, k)+T(n-1, k-1)+T(n-1, k-2) starting with T(0, 0)=1. See A027907 for more.
As a number triangle, T(n, k)=sum{i=0..floor((n-k)/2), C(n-k-i, i)C(k, n-k-i)}; - Paul Barry (pbarry(AT)wit.ie), Apr 26 2005
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EXAMPLE
| Rows start 1,0,0,0,0,0,...; 1,1,1,0,0,0,0,...; 1,2,3,2,1,0,0,...; 1,3,6,7,6,3,1,0,...; 1,4,10,16,19,16,10,4,1,...; etc.
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CROSSREFS
| Visible version of A027907. Row sums are 3^n, i.e. A000244. Central diagonal is A002426. Cf. A071676 for a slight variation.
Sequence in context: A173402 A055334 A106237 * A034365 A103778 A099423
Adjacent sequences: A071672 A071673 A071674 * A071676 A071677 A071678
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), May 30 2002
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