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A152904 Triangle read by rows: T(n,k) = A008683(n-k+1); 1<=k<=n; mu(n) "decrescendo". 1
1, -1, 1, -1, -1, 1, 0, -1, -1, 1, -1, 0, -1, -1, 1, 1, -1, 0, -1, -1, 1, -1, 1, -1, 0, -1, -1, 1, 0, -1, 1, -1, 0, -1, -1, 1, 0, 0, -1, 1, -1, 0, -1, -1, 1, 1, 0, 0, -1, 1, -1, 0, -1, -1, 1, -1, 1, 0, 0, -1, 1, -1, 0, -1, -1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..66.

E. Deutsch, L. Ferrari and S. Rinaldi, Production Matrices, Advances in Applied Mathematics, 34 (2005) pp. 101-122.

FORMULA

Triangle read by rows, T(n,k) = A008683(n-k+1) = A008683 in every column = A008683 "decrescendo"d by rows.

EXAMPLE

Triangle begins

   1;

  -1, 1;

  -1, -1, 1;

   0, -1, -1, 1;

  -1, 0, -1, -1, 1;

   1, -1, 0, -1, -1, 1;

  -1, 1, -1, 0, -1, -1, 1;

   0, -1, 1, -1, 0, -1, -1, 1;

   0, 0, -1, 1, -1, 0, -1, -1, 1;

   ...

Production matrix begins

  -1, 1,

  -2, 0, 1,

  -3, 0, 0, 1,

  -6, 0, 0, 0, 1,

  -9, 0, 0, 0, 0, 1,

  -17, 0, 0, 0, 0, 0, 1,

  -28, 0, 0, 0, 0, 0, 0, 1,

  -50, 0, 0, 0, 0, 0, 0, 0, 1,

  -83, 0, 0, 0, 0, 0, 0, 0, 0, 1,

  -147, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ...

  where first column is -A073776(n+1). - Paul Barry, Feb 10 2011

CROSSREFS

Cf. A008683, A002321, A073776, A152901, A152902.

Row sums = A002321, the Mertens function. A185694 is an eigensequence.

Sequence in context: A276254 A303300 A249865 * A249133 A118102 A089509

Adjacent sequences:  A152901 A152902 A152903 * A152905 A152906 A152907

KEYWORD

tabl,sign

AUTHOR

Gary W. Adamson, Dec 14 2008

STATUS

approved

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Last modified July 25 19:05 EDT 2021. Contains 346291 sequences. (Running on oeis4.)