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Search: id:A104402
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| 1, -1, 1, 1, -2, 1, 0, 2, -3, 1, 0, -1, 4, -4, 1, 0, 0, -3, 7, -5, 1, 0, 0, 1, -7, 11, -6, 1, 0, 0, 0, 4, -14, 16, -7, 1, 0, 0, 0, -1, 11, -25, 22, -8, 1, 0, 0, 0, 0, -5, 25, -41, 29, -9, 1, 0, 0, 0, 0, 1, -16, 50, -63, 37, -10, 1, 0, 0, 0, 0, 0, 6, -41, 91, -92, 46, -11, 1, 0, 0, 0, 0, 0, -1, 22, -91, 154, -129, 56, -12, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are all zeros for n>0. Absolute row sums form 2*A000045(n+1) for n>0, where A000045 = Fibonacci numbers. Sums of squared terms in row n = 2*A003440(n) for n>0, where A003440 = number of binary vectors with restricted repetitions.
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FORMULA
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G.f.: (1-x+x^2)/(1-x*y*(1-x)). T(n, k) = T(n-1, k-1) - T(n-2, k-1) for k>0 with T(0, 0)=1, T(1, 0)=-1, T(2, 0)=1, T(n, 0)=0 (n>2).
T(n, k) = (-1)^(n-k)*(C(k, n-k) + C(k+1, n-k-1)) for n>0, with T(0, 0)=1.
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EXAMPLE
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Rows begin:
1;
-1,1;
1,-2,1;
0,2,-3,1;
0,-1,4,-4,1;
0,0,-3,7,-5,1;
0,0,1,-7,11,-6,1;
0,0,0,4,-14,16,-7,1;
0,0,0,-1,11,-25,22,-8,1; ...
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PROGRAM
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(PARI) {T(n, k)=local(X=x+x*O(x^n), Y=y+y*O(y^k)); polcoeff(polcoeff((1-X+X^2)/(1-X*Y*(1-X)), n, x), k, y)} (PARI) {T(n, k)=if(n<k|k<0, 0, if(n==k, 1, if(n==1&k==0, -1, if(n==2&k==0, 1, T(n-1, k-1)-T(n-2, k-1)))))}
(PARI) T(n, k)=(-1)^(n-k)*(binomial(k, n-k)+binomial(k+1, n-k-1))
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CROSSREFS
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Cf. A091491, A000045, A003440.
Sequence in context: A037181 A051070 A104041 this_sequence A131084 A123949 A004718
Adjacent sequences: A104399 A104400 A104401 this_sequence A104403 A104404 A104405
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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), Mar 05 2005
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