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A154990 Triangle read by rows. Main diagonal is positive. The rest of the terms are negative. 8
1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Triangle can be used in matrix inverses. Signs in columns as in A153881.

Iff n is a triangular number, a(n)=1; otherwise, a(n)=-1. (This is explicitly implemented in the second Mathematica program below.) - Harvey P. Dale, Apr 27 2014

LINKS

G. C. Greubel, Rows n = 1..30 of the triangle, flattened

FORMULA

From G. C. Greubel, Mar 06 2021: (Start)

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

Sum_{k=1..n} T(n, k) = 2-n = -A023443(n-1) = -A023444(n). (End)

EXAMPLE

Table begins:

1;

-1, 1;

-1, -1, 1;

-1, -1, -1, 1;

-1, -1, -1, -1, 1;

-1, -1, -1, -1, -1, 1;

-1, -1, -1, -1, -1, -1, 1;

MAPLE

A154990 := proc(n, k)

option remember;

if k = n then

1;

elif k > n then

0;

else

-1 ;

end if;

end proc:

seq(seq(A154990(n, k), k=1..n), n=1..12) ; # R. J. Mathar, Sep 16 2017

MATHEMATICA

Flatten[Table[PadLeft[{1}, n, -1], {n, 15}]] (* or *) With[{tr=Accumulate[ Range[ 15]]}, Table[If[MemberQ[tr, n], 1, -1], {n, Last[tr]}]] (* Harvey P. Dale, Apr 27 2014 *)

PROG

(Sage) flatten([[1 if k==n else -1 for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Mar 06 2021

(Magma) [k eq n select 1 else -1: k in [1..n], n in [1..12]]; // G. C. Greubel, Mar 06 2021

CROSSREFS

Cf. A023443, A023444.

Sequence in context: A057077 A262725 A070748 * A209615 A242179 A319117

Adjacent sequences: A154987 A154988 A154989 * A154991 A154992 A154993

KEYWORD

sign,easy,tabl

AUTHOR

Mats Granvik, Jan 18 2009

STATUS

approved

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Last modified February 2 06:25 EST 2023. Contains 360000 sequences. (Running on oeis4.)