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A118404
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Triangle T, read by rows, where all columns of T are different and yet all columns of the matrix square T^2 (A118407) are equal; also equals the matrix inverse of triangle A118400.
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4
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1, 1, -1, -1, 0, 1, -1, 1, -1, -1, 1, 0, 0, 2, 1, 1, -1, 0, -2, -3, -1, -1, 0, 1, 2, 5, 4, 1, -1, 1, -1, -3, -7, -9, -5, -1, 1, 0, 0, 4, 10, 16, 14, 6, 1, 1, -1, 0, -4, -14, -26, -30, -20, -7, -1, -1, 0, 1, 4, 18, 40, 56, 50, 27, 8, 1, -1, 1, -1, -5, -22, -58, -96, -106, -77, -35, -9, -1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,14
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FORMULA
| G.f.: A(x,y) = (1+x)^2/(1+x^2)/(1+x+x*y). G.f. of column k = (-1)^k/(1+x^2)/(1+x)^(k-1) for k>=0.
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EXAMPLE
| Triangle begins:
1;
1,-1;
-1, 0, 1;
-1, 1,-1,-1;
1, 0, 0, 2, 1;
1,-1, 0,-2,-3,-1;
-1, 0, 1, 2, 5, 4, 1;
-1, 1,-1,-3,-7,-9,-5,-1;
1, 0, 0, 4, 10, 16, 14, 6, 1;
1,-1, 0,-4,-14,-26,-30,-20,-7,-1;
-1, 0, 1, 4, 18, 40, 56, 50, 27, 8, 1;
-1, 1,-1,-5,-22,-58,-96,-106,-77,-35,-9,-1;
1, 0, 0, 6, 27, 80, 154, 202, 183, 112, 44, 10, 1; ...
The matrix square is A118407:
1;
0, 1;
-2, 0, 1;
2,-2, 0, 1;
0, 2,-2, 0, 1;
-2, 0, 2,-2, 0, 1;
4,-2, 0, 2,-2, 0, 1;
-6, 4,-2, 0, 2,-2, 0, 1;
4,-6, 4,-2, 0, 2,-2, 0, 1;
6, 4,-6, 4,-2, 0, 2,-2, 0, 1; ...
in which all columns are equal.
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PROG
| (PARI) {T(n, k)=polcoeff(polcoeff((1+x)^2/(1+x^2)/(1+x+x*y +x*O(x^n)), n, x)+y*O(y^k), k, y)}
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CROSSREFS
| Cf. A118405 (row sums), A118406 (unsigned row sums), A118407 (matrix square), A118400 (matrix inverse).
Sequence in context: A064272 A200650 A117479 * A089339 A127284 A120691
Adjacent sequences: A118401 A118402 A118403 * A118405 A118406 A118407
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KEYWORD
| sign,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 27 2006
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