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Search: id:A124928
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| A124928 |
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Triangle read by rows: T(n,0)=1, T(n,k)=3*binom(n,k) if k>=0 (0<=k<=n). |
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+0
3
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| 1, 1, 3, 1, 6, 3, 1, 9, 9, 3, 1, 12, 18, 12, 3, 1, 15, 30, 30, 15, 3, 1, 18, 45, 60, 45, 18, 3, 1, 21, 63, 105, 105, 63, 21, 3, 1, 24, 84, 168, 210, 168, 84, 24, 3, 1, 27, 108, 252, 378, 378, 252, 108, 27, 3, 1, 30, 135, 360, 630, 756, 630, 360, 135, 30, 3, 1, 33, 165, 495, 990
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sums = A033484: (1, 4, 10, 22, 46, 94...); 3*2^n - 2. Analogous triangle using (1,2,2,2...) as the main diagonal of M = A124927.
Except for the first column, entries in the Pascal triangle are tripled.
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FORMULA
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G.f.= G(t,z)=3/[1-(1+t)*z]-2/(1-z).
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EXAMPLE
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First few rows of the triangle are:
1;
1, 3;
1, 6, 3;
1, 9, 9, 3;
1, 12, 18, 12, 3;
1, 15, 30, 30, 15, 3;
1, 18, 45, 60, 45, 18, 3;
...
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MAPLE
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T:=proc(n, k) if k=0 then 1 else 3*binomial(n, k) fi end: for n from 0 to 12 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A033484, A124927.
Sequence in context: A072361 A145366 A145367 this_sequence A122432 A131110 A133093
Adjacent sequences: A124925 A124926 A124927 this_sequence A124929 A124930 A124931
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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), Nov 12 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 29 2006
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