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Search: id:A131086
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| A131086 |
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Triangle read by rows: T(n,k)=2*binom(n,k)-(-1)^(n-k) (0<=k<=n). |
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+0
2
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| 1, 3, 1, 1, 5, 1, 3, 5, 7, 1, 1, 9, 11, 9, 1, 3, 9, 21, 19, 11, 1, 1, 13, 29, 41, 29, 13, 1, 3, 13, 43, 69, 71, 41, 15, 1, 1, 17, 55, 113, 139, 113, 55, 17, 1, 3, 17, 73, 167, 253, 251, 169, 71, 19, 1, 1, 21, 89, 241, 419, 505, 419, 241, 89, 21, 1, 3, 21, 111, 329
(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 = A051049 starting (1, 4, 7, 16, 31, 64,...).
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FORMULA
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G.f.=G(t,z)=(1+3z-tz-2tz^2)/[(1+z)(1-tz)(1-z-tz)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 21 2007
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EXAMPLE
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First few rows of the triangle are:
1;
3, 1;
1, 5, 1;
3, 5, 7, 1;
1, 9, 11, 9, 1;
3, 9, 21, 19, 11, 1;
1, 13, 29, 41, 29, 13, 1;
...
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MAPLE
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T := proc (n, k) if k <= n then 2*binomial(n, k)-(-1)^(n-k) else 0 end if end proc: for n from 0 to 11 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 21 2007
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CROSSREFS
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Cf. A000012, A051049.
Sequence in context: A046230 A046229 A124738 this_sequence A069002 A076334 A014475
Adjacent sequences: A131083 A131084 A131085 this_sequence A131087 A131088 A131089
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 14 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 21 2007
Sequence corrected by njas, Sep 30 2007
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