OFFSET
0,4
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
Sum_{=0..n} T(n, k) = A032925(n).
T(n, 0) = A115639(n).
T(n, k) = 1 if n = k, otherwise T(n, k) = (-1)*Sum_{j=k+1..n} T(n, j)*A115713(j, k). - R. J. Mathar, Sep 07 2016
EXAMPLE
Triangle begins
1;
1, 1;
4, 0, 1;
4, 0, 1, 1;
4, 4, 0, 0, 1;
4, 4, 0, 0, 1, 1;
16, 0, 4, 0, 0, 0, 1;
16, 0, 4, 0, 0, 0, 1, 1;
16, 0, 4, 4, 0, 0, 0, 0, 1;
16, 0, 4, 4, 0, 0, 0, 0, 1, 1;
16, 16, 0, 0, 4, 0, 0, 0, 0, 0, 1;
16, 16, 0, 0, 4, 0, 0, 0, 0, 0, 1, 1;
16, 16, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 1;
16, 16, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 1, 1;
64, 0, 16, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1;
64, 0, 16, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 1;
64, 0, 16, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1;
MAPLE
A115715 := proc(n, k)
option remember;
if n = k then
1;
elif k > n then
0;
else
-add(procname(n, l)*A115713(l, k), l=k+1..n) ;
end if;
end proc:
seq(seq(A115715(n, k), k=0..n), n=0..13) ; # R. J. Mathar, Sep 07 2016
MATHEMATICA
A115713[n_, k_]:= If[k==n, 1, If[k==n-1, ((-1)^n-1)/2, If[n==2*k+2, -4, 0]]];
T[n_, k_]:= T[n, k]= If[k==n, 1, -Sum[T[n, j]*A115713[j, k], {j, k+1, n}]];
Table[T[n, k], {n, 0, 18}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 23 2021 *)
PROG
(Sage)
@CachedFunction
def A115713(n, k):
if (k==n): return 1
elif (k==n-1): return -(n%2)
elif (n==2*k+2): return -4
else: return 0
def A115715(n, k):
if (k==0): return 4^(floor(log(n+2, 2)) -1)
elif (k==n): return 1
elif (k==n-1): return (n%2)
flatten([[A115715(n, k) for k in (0..n)] for n in (0..18)]) # G. C. Greubel, Nov 23 2021
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Jan 29 2006
STATUS
approved