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Search: id:A131065
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| A131065 |
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Triangle read by rows: T(n,k)=6*binom(n,k)-5 (0<=k<=n). |
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+0
9
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| 1, 1, 1, 1, 7, 1, 1, 13, 13, 1, 1, 19, 31, 19, 1, 1, 25, 55, 55, 25, 1, 1, 31, 85, 115, 85, 31, 1, 1, 37, 121, 205, 205, 121, 37, 1, 1, 43, 163, 331, 415, 331, 163, 43, 1, 1, 49, 211, 499, 751, 751, 499, 211, 49, 1, 1, 55, 265, 715, 1255, 1507, 1255, 715, 265, 55, 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 = A131066: (1, 2, 9, 28, 71, 162, 349,...), the binomial transform of (1, 1, 6, 6, 6,...).
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FORMULA
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G.f.=G(t,z)=(1-z-tz+6tz^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, 7, 1;
1, 13, 13, 1;
1, 19, 31, 19, 1;
1, 25, 55, 55, 25, 1;
...
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MAPLE
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T := proc (n, k) if k <= n then 6*binomial(n, k)-5 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. A109128, A131060, A131061, A131062, A131063, A131064, A131066.
Sequence in context: A105395 A120437 A050179 this_sequence A081580 A082110 A141597
Adjacent sequences: A131062 A131063 A131064 this_sequence A131066 A131067 A131068
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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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