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A154990
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Triangle read by rows. Main diagonal is positive. The rest of the terms are negative.
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8
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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)
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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G. C. Greubel, Rows n = 1..30 of the triangle, flattened
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FORMULA
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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)
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EXAMPLE
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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;
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A023443, A023444.
Sequence in context: A057077 A262725 A070748 * A209615 A242179 A319117
Adjacent sequences: A154987 A154988 A154989 * A154991 A154992 A154993
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KEYWORD
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sign,easy,tabl
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AUTHOR
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Mats Granvik, Jan 18 2009
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STATUS
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approved
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