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.
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
KEYWORD
AUTHOR
Mats Granvik, Jan 18 2009
STATUS
approved