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Search: id:A102587
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| A102587 |
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Triangular matrix, read by rows, equal to the matrix inverse of triangle A094531, which is the right-hand side of trinomial table A027907. |
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+0
8
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| 1, -1, 1, -1, -2, 1, 2, 0, -3, 1, -1, 4, 2, -4, 1, -1, -5, 5, 5, -5, 1, 2, 0, -12, 4, 9, -6, 1, -1, 7, 7, -21, 0, 14, -7, 1, -1, -8, 12, 24, -30, -8, 20, -8, 1, 2, 0, -27, 9, 54, -36, -21, 27, -9, 1, -1, 10, 15, -60, -15, 98, -35, -40, 35, -10, 1, -1, -11, 22, 66, -99, -77, 154, -22, -66, 44, -11, 1, 2, 0, -48, 16, 180, -120, -196, 216, 9
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Riordan array ((1-x^2)/(1+x+x^2),x/(1+x+x^2)). - Paul Barry (pbarry(AT)wit.ie), Jul 14 2005
Inverse of A094531. Rows sums are 1,0,-2,0,2,0,-2,... with g.f. (1-x^2)/(1+x^2). Diagonal sums are (-1)^n*C(1,n) with g.f. 1-x. - Paul Barry (pbarry(AT)wit.ie), Jul 14 2005
Row sums form the period 4 sequence: {1, 0,-2,0,2, 0,-2,0,2, ...}. Absolute row sums form A102588.
Sum_{k=0..n} T(n,k)^2 = 2*A002426(n) for n>0.
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EXAMPLE
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Rows begin:
[1],
[ -1,1],
[ -1,-2,1],
[2,0,-3,1],
[ -1,4,2,-4,1],
[ -1,-5,5,5,-5,1],
[2,0,-12,4,9,-6,1],
[ -1,7,7,-21,0,14,-7,1],
[ -1,-8,12,24,-30,-8,20,-8,1],
[2,0,-27,9,54,-36,-21,27,-9,1],
[ -1,10,15,-60,-15,98,-35,-40,35,-10,1],
[ -1,-11,22,66,-99,-77,154,-22,-66,44,-11,1],...
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PROGRAM
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(PARI) {T(n, k)=local(A); A=matrix(n+1, n+1, r, c, if(r<c-1, 0, polcoeff((1+x+x^2)^(r-1), r+c-2))); return((A^-1)[n+1, k+1])}
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CROSSREFS
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Cf. A094531, A102588.
Sequence in context: A071485 A127969 A081733 this_sequence A119387 A055941 A068076
Adjacent sequences: A102584 A102585 A102586 this_sequence A102588 A102589 A102590
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KEYWORD
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sign,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 22 2005
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