OFFSET
0,1
COMMENTS
Triangle T(n,k), 0 <= k <= n, read by rows given by [ -1, 2, 0, 0, 0, 0, 0, ...] DELTA [1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, May 01 2007
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10010 (Rows 0 <= n <= 140)
FORMULA
T(n,k) = 1 if k = n, -1 if k = 0, otherwise 0.
Sum_{k=0..n} T(n, k) = 0^n (row sums).
Sum_{k=0..floor(n/2)} T(n-k, k) = 0^n - (1-(-1)^n)/2 (diagonal sums).
G.f.: (1 - 2*x + y*x^2)/((1-x)*(1-y*x)). - Philippe Deléham, Feb 11 2012
EXAMPLE
Triangle begins
1;
-1, 1;
-1, 0, 1;
-1, 0, 0, 1;
-1, 0, 0, 0, 1;
-1, 0, 0, 0, 0, 1;
-1, 0, 0, 0, 0, 0, 1;
-1, 0, 0, 0, 0, 0, 0, 1;
-1, 0, 0, 0, 0, 0, 0, 0, 1;
-1, 0, 0, 0, 0, 0, 0, 0, 0, 1;
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
Production matrix begins
-1, 1;
-2, 1, 1;
-2, 1, 0, 1;
-2, 1, 0, 0, 1;
-2, 1, 0, 0, 0, 1;
-2, 1, 0, 0, 0, 0, 1;
-2, 1, 0, 0, 0, 0, 0, 1;
-2, 1, 0, 0, 0, 0, 0, 0, 1;
MATHEMATICA
Table[Range[n] /. {k_ /; k == 1 && n != 1 -> -1, k_ /; k == n -> 1, _Integer -> 0}, {n, 15}] // Flatten (* Michael De Vlieger, Jul 21 2016 *)
PROG
(Sage) flatten([[1 if k==n else -1 if k==0 else 0 for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Jun 18 2021
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Feb 06 2005
STATUS
approved