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Search: id:A131063
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| A131063 |
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Triangle read by rows: T(n,k)=5*binom(n,k)-4 (0<=k<=n). |
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+0
9
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| 1, 1, 1, 1, 6, 1, 1, 11, 11, 1, 1, 16, 26, 16, 1, 1, 21, 46, 46, 21, 1, 1, 26, 71, 96, 71, 26, 1, 1, 31, 101, 171, 171, 101, 31, 1, 1, 36, 136, 276, 346, 276, 136, 36, 1, 1, 41, 176, 416, 626, 626, 416, 176, 41, 1, 1, 46, 221, 596, 1046, 1256, 1046, 596, 221, 46, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums = A131064: (1, 2, 8, 24, 60, 136, 292,...), the binomial transform of (1, 1, 5, 5, 5,...).
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FORMULA
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G.f.=G(t,z)=(1-z-tz+5tz^2)/[(1-z)(1-tz)(1-z-tz)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 20 2007
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
1, 6, 1;
1, 11, 11, 1;
1, 16, 26, 16, 1;
1, 21, 46, 46, 21, 1;
1, 26, 71, 96, 71, 26, 1;
...
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MAPLE
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T := proc (n, k) if k <= n then 5*binomial(n, k)-4 else 0 end if end proc: for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 20 2007
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CROSSREFS
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Cf. A131060, A131061, A131062, A131064, A131065, A131066.
Sequence in context: A144395 A046621 A046617 this_sequence A081579 A146772 A082105
Adjacent sequences: A131060 A131061 A131062 this_sequence A131064 A131065 A131066
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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 13 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 20 2007
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