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A102547
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Triangle read by rows, formed from antidiagonals of the antidiagonals (A011973) of Pascal's triangle (A007318).
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1
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1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 4, 1, 1, 5, 3, 1, 6, 6, 1, 7, 10, 1, 1, 8, 15, 4, 1, 9, 21, 10, 1, 10, 28, 20, 1, 1, 11, 36, 35, 5, 1, 12, 45, 56, 15, 1, 13, 55, 84, 35, 1, 1, 14, 66, 120, 70, 6, 1, 15, 78, 165, 126, 21, 1, 16, 91, 220, 210, 56, 1, 1, 17, 105, 286, 330, 126, 7, 1, 18, 120
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| Row sums are A000930, antidiagonal sums are A003269.
Row n contains 1+floor(n/3) terms.
Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 15 2010: (Start)
T(n,k) is the number of compositions of n+3 with k+1 parts, all at least 3. Example: T(9,2)=binom(5,2)=10 because we have 336, 363, 633, 345, 354, 435, 453, 534, 543, and 444.
(End)
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FORMULA
| Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 15 2010: (Start)
T(n,k)=binom(n-2k,k) (0<=k<=n/3).
(End)
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EXAMPLE
| Triangle begins:
1;
1;
1;
1,1;
1,2;
1,3;
1,4,1;
1,5,3;
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MAPLE
| for n from 0 to 20 do seq(binomial(n-2*k, k), k = 0 .. floor((1/3)*n)) end do; # yields sequence in triangular form [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 15 2010]
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CROSSREFS
| Cf. A007318 A011973 A003269 A000930.
Sequence in context: A195837 A123539 A142593 * A177812 A087267 A128267
Adjacent sequences: A102544 A102545 A102546 * A102548 A102549 A102550
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KEYWORD
| nonn,tabf
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AUTHOR
| Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Feb 24 2005
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