OFFSET
1,2
COMMENTS
Equivalently, (lower left) triangle M^2 = transpose(T)^2. The following description refers to the lower triangular version, but OEIS's "TABL" link displays the values more appropriately as an upper right triangle. - M. F. Hasler, Apr 18 2009
For n rows, use matrices in each row from the sequence 1, -3, 5, -7, ... (filling in with zeros except for the n-th row). Let the matrix = M, then square and delete the zeros. For example, the 3-row generator would be [1 0 0 / 1 -3 0 / 1 -3 5] = M. The nonzero elements of M^2 give the first 6 terms of the sequence.
FORMULA
Diagonal elements are the odd squares: a(k(k+1)/2)=(2k+1)^2. First element in row k is (-1)^k*k. - M. F. Hasler, Apr 18 2009
EXAMPLE
The matrix
[ 1 0 0 0 ...]
[ 1 -3 0 0 ...]
[ 1 -3 5 0 ...]
[ 1 -3 5 -7 ...]
squared yields
[ +1 0 0 0 ...]
[ -2 +9 0 0 ...]
[ +3 -6 25 0 ...]
[ -4 15 -10 49 ...]; the lower left triangle gives this sequence: 1; -2, 9; 3, -6, 25; ...
PROG
(PARI) T=matrix(12, 12, i, j, if(j>=i, (-1)^i*(1-2*i)))^2; concat(vector(#T, i, vecextract(T[, i], 2^i-1))) \\ M. F. Hasler, Apr 18 2009
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Gary W. Adamson, Jun 07 2004
EXTENSIONS
Edited and extended by M. F. Hasler, Apr 18 2009
STATUS
approved