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Search: id:A112906
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| A112906 |
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A skew generalized Pascal triangle. |
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+0
3
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| 1, 0, 3, 0, 1, 10, 0, 0, 6, 33, 0, 0, 1, 29, 109, 0, 0, 0, 9, 126, 360, 0, 0, 0, 1, 57, 516, 1189, 0, 0, 0, 0, 12, 306, 2034, 3927, 0, 0, 0, 0, 1, 94, 1491, 7807, 12970, 0, 0, 0, 0, 0, 15, 600, 6813, 29382, 42837, 0, 0, 0, 0, 0, 1, 140, 3385, 29737, 108923, 141481, 0, 0, 0, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Main diagonal is A006190. Row sums are A007482. Column sums are A001076(n+1). Compare with [0,1/3,-1/3,0,0,..] DELTA [3,1/3,-1/3,0,0,...] where DELTA is the operator defined in A084938. A skewed version of the Riordan array (1/(1-3x-x^2),x/(1-3x-x^2)).
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FORMULA
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G.f.: 1/(1-3xy(1+x/3)-x^2*y^2); T(n, k)=sum{j=0..floor((2k-n)/2), C(k-j, n-k)C(2k-n, j)3^(2k-2j-n)}; T(n, k) = 3*T(n-1, k-1)+T(n-2, k-1)+T(n-2, k-2).
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EXAMPLE
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Triangle begins
1;
0, 3;
0, 1, 10;
0, 0, 6, 33;
0, 0, 1, 29, 109;
0, 0, 0, 9, 126, 360,
0, 0, 0, 1, 57, 516, 1189;
0, 0, 0, 0, 12, 306, 2034, 3927;
0, 0, 0, 0, 1, 94, 1491, 7809, 12970;
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CROSSREFS
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Cf. A112899.
Sequence in context: A152150 A136239 A058175 this_sequence A137375 A145881 A135313
Adjacent sequences: A112903 A112904 A112905 this_sequence A112907 A112908 A112909
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 05 2005
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