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A128132 A natural number transform, companion to A127701. 11
1, -1, 2, 0, -1, 3, 0, 0, -1, 4, 0, 0, 0, -1, 5, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, 0, -1, 7, 0, 0, 0, 0, 0, 0, -1, 8, 0, 0, 0, 0, 0, 0, 0, -1, 9, 0, 0, 0, 0, 0, 0, 0, 0, -1, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Binomial transform is A128133.

LINKS

Table of n, a(n) for n=1..78.

FORMULA

T(n,n) = n.

T(n,n-1) = -1.

T(n,k) = 0 for k <> n, n-1.

EXAMPLE

Triangle T(n,k) (with rows n >= 1 and columns k = 1..n) begins:

   1;

  -1,  2;

   0, -1,  3;

   0,  0, -1,  4;

   0,  0,  0, -1,  5;

   0,  0,  0,  0, -1, 6;

   ...

MAPLE

A128132 := proc(n, k)

    if n = k then

        n;

    elif k = n-1 then

        -1 ;

    else

        0 ;

    end if;

end proc: # R. J. Mathar, Apr 26 2016

MATHEMATICA

{1}~Join~Table[PadLeft[{-1, n}, n], {n, 2, 12}] // Flatten (* Michael De Vlieger, Apr 26 2016 *)

CROSSREFS

Cf. A127701, A128133, A128134.

Sequence in context: A085855 A280500 A309576 * A158821 A127701 A004199

Adjacent sequences:  A128129 A128130 A128131 * A128133 A128134 A128135

KEYWORD

tabl,sign,easy,changed

AUTHOR

Gary W. Adamson, Feb 15 2007

STATUS

approved

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Last modified August 4 16:34 EDT 2020. Contains 336202 sequences. (Running on oeis4.)