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A103451
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Triangular array T read by rows: T(n, 1) = T(n, n) = 1, T(n, k) = 0 for 1 < k < n.
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28
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1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Equals Pascal's triangle (A007318) where all elements > 1 are replaced with zero. Therefore it might be called "binomial skeleton".
Row sums are in A040000, antidiagonal sums are in A040001. When construed as a lower triangular matrix, the matrix inverse is A103452.
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FORMULA
| a(n) = A097806(n-1) for n > 0. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 16 2007
T(n,k) = C(n,k-n)+C(n,-k)-C(0,n+k), 0<=k<=n. [From Eric Werley, Jul 1 2011]
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EXAMPLE
| First few rows are
[ 1 ],
[ 1, 1 ],
[ 1, 0, 1 ],
[ 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 1 ].
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PROG
| (MAGMA) r:=14; T:=ScalarMatrix(r, 1); for n in [1..r] do T[n, 1]:=1; end for; &cat[ [ T[n, k]: k in [1..n] ]: n in [1..r] ];
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CROSSREFS
| Cf. A007318, A040000, A040001, A103452, A097806.
Sequence in context: A174852 A065333 A127972 * A103452 A131219 A127970
Adjacent sequences: A103448 A103449 A103450 * A103452 A103453 A103454
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 06 2005
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EXTENSIONS
| Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 26 2011
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