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Search: id:A124860
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| A124860 |
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A Jacobsthal-Pascal triangle. |
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+0
3
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| 1, 1, 1, 3, 6, 3, 5, 15, 15, 5, 11, 44, 66, 44, 11, 21, 105, 210, 210, 105, 21, 43, 258, 645, 860, 645, 258, 43, 85, 595, 1785, 2975, 2975, 1785, 595, 85, 171, 1368, 4788, 9576, 11970, 9576, 4788, 1368, 171, 341, 3069, 12276, 28644
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums are A003683(n+1). Diagonal sums are A124861. Central coefficients are A124862.
Triangle T(n,k) read by rows given by [1, 2, -2, 0, 0, 0, ...] DELTA [1, 2, -2, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 11 2006
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FORMULA
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G.f.: 1/(1-x(1+y)-2x^2(1+y)^2); Number triangle T(n,k)=J(n+1)*C(n,k), J(n)=A001045(n);
T(n,k)=T(n-1,k-1)+T(n-1,k)+2*T(n-2,k-2)+4*T(n-2,k-1)+2*T(n-2,k), T(0,0)=1, T(n,k)=0 if k<0 or if k>n . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 11 2006
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EXAMPLE
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Triangle begins
1,
1, 1,
3, 6, 3,
5, 15, 15, 5,
11, 44, 66, 44, 11,
21, 105, 210, 210, 105, 21,
43, 258, 645, 860, 645, 258, 43
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CROSSREFS
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Cf. A016095.
Sequence in context: A111762 A072971 A134548 this_sequence A038138 A010704 A123146
Adjacent sequences: A124857 A124858 A124859 this_sequence A124861 A124862 A124863
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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), Nov 10 2006
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