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A112883
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A skew Jacobsthal-Pascal matrix.
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1
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1, 0, 1, 0, 1, 3, 0, 0, 2, 5, 0, 0, 1, 7, 11, 0, 0, 0, 3, 16, 21, 0, 0, 0, 1, 12, 41, 43, 0, 0, 0, 0, 4, 34, 94, 85, 0, 0, 0, 0, 1, 18, 99, 219, 171, 0, 0, 0, 0, 0, 5, 60, 261, 492, 341, 0, 0, 0, 0, 0, 1, 25, 195, 678, 1101, 683, 0, 0, 0, 0, 0, 0, 6, 95, 576, 1692, 2426, 1365, 0, 0, 0, 0, 0
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OFFSET
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0,6
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COMMENTS
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T(n,n) is A001045(n), row sums are A006130, column sums are A002605. Compare with [0,1,-1,0,0,..] DELTA [1,2,-2,0,0,...] where DELTA is the operator defined in A084938. A skewed version of the Riordan array (1/(1-x-2x^2),x/(1-x-2x^2)) (A073370).
Modulo 2, this sequence gives A106344 . [From Philippe DELEHAM, Dec 18 2008]
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LINKS
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Table of n, a(n) for n=0..82.
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FORMULA
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G.f.: 1/(1-yx(1-x)-2x^2*y*2); Number triangle T(n, k)=sum{j=0..2k-n, C(n-k+j, n-k)C(j, 2k-n-j)2^(2k-n-j)}; T(n, k)=A073370(k, n-k); T(n, k) = T(n-1, k-1) + T(n-2, k-1) +2*T(n-2, k-2) (Philippe Deleham).
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EXAMPLE
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Rows begin
1;
0, 1;
0, 1, 3;
0, 0, 2, 5;
0, 0, 1, 7, 11;
0, 0, 0, 3, 16, 21;
0, 0, 0, 1, 12, 41, 43;
0, 0, 0, 0, 4, 34, 94, 85;
0, 0, 0, 0, 1, 18, 99, 219, 171;
0, 0, 0, 0, 0, 5, 60, 261, 492, 341;
0, 0, 0, 0, 0, 1, 25, 195, 678, 1101, 683;
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CROSSREFS
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Cf. A111006.
Sequence in context: A108930 A059682 A156548 * A117138 A095104 A021337
Adjacent sequences: A112880 A112881 A112882 * A112884 A112885 A112886
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry, Oct 05 2005
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STATUS
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approved
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