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A140182
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Binomial transform of an infinite bidiagonal matrix with (1,3,1,3,1,3,...) in the main diagonal, (1,1,1,...) in the subdiagonal, the rest zeros.
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1
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1, 2, 3, 3, 7, 1, 4, 12, 4, 3, 5, 18, 10, 13, 1, 6, 25, 20, 35, 6, 3, 7, 33, 35, 75, 21, 19, 1, 8, 42, 56, 140, 56, 70, 8, 3, 9, 52, 84, 238, 126, 196, 36, 25, 1, 10, 63, 120, 378, 252, 462, 120, 117, 10, 3, 11, 75, 165, 570, 462, 966, 330, 405, 55, 31, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row sums = A052940: (1, 5, 11, 23, 47, 95,...).
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FORMULA
| A007318 as an infinite lower triangular matrix * a bidiagonal matrix with (1,3,1,3,1,3,...) in the main diagonal, (1,1,1,...) in the subdiagonal and the rest zeros.
T(n,2k)=binom(n+1,2k+1); T(n,2k+1)=2*binom(n,2k+1)+binom(n+1,2k+2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 18 2008
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EXAMPLE
| First few rows of the triangle are:
1;
2, 3;
3, 7, 1;
4, 12, 4, 3;
5, 18, 10, 13, 1;
6, 25, 20, 35, 6, 3;
7, 33, 35, 75 21, 19, 1;
...
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MAPLE
| T:=proc(n, k) if `mod`(k, 2)=0 then binomial(n+1, k+1) else 2*binomial(n, k)+binomial(n+1, k+1) end if end proc: for n from 0 to 10 do seq(T(n, k), k=0..n) end do; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 18 2008
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CROSSREFS
| Cf. A052940.
Sequence in context: A028257 A100228 A111003 * A082910 A023646 A056225
Adjacent sequences: A140179 A140180 A140181 * A140183 A140184 A140185
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 11 2008
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