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A131061
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Triangle read by rows: T(n,k)=4*binom(n,k)-3 (0<=k<=n).
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11
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1, 1, 1, 1, 5, 1, 1, 9, 9, 1, 1, 13, 21, 13, 1, 1, 17, 37, 37, 17, 1, 1, 21, 57, 77, 57, 21, 1, 1, 25, 81, 137, 137, 81, 25, 1, 1, 29, 109, 221, 277, 221, 109, 29, 1, 1, 33, 141, 333, 501, 501, 333, 141, 33, 1, 1, 37, 177, 477, 837, 1005, 837, 477, 177, 37, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums = A131062: (1, 2, 7, 20, 49, 110, 235,...); the binomial transform of (1, 1, 4, 4, 4,...).
4*A007318 - 3*A000012 as infinite lower triangular matrices. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 21 2007
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FORMULA
| G.f.=G(t,z)=(1-z-tz+4tz^2)/[(1-z)(1-tz)(1-z-tz)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 21 2007
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EXAMPLE
| First few rows of the triangle are:
1;
1, 1;
1, 5, 1;
1, 9, 9, 1;
1, 13, 21, 13, 1;
1, 17, 37, 37, 17, 1;
1, 21, 57, 77, 57, 21, 1;
...
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MAPLE
| T := proc (n, k) if k <= n then 4*binomial(n, k)-3 else 0 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), Jun 21 2007
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CROSSREFS
| Cf. A131060, A131062, A131063, A131064, A131065, A131066.
Sequence in context: A153108 A157174 A183450 * A157169 A081578 A184883
Adjacent sequences: A131058 A131059 A131060 * A131062 A131063 A131064
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 21 2007
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