OFFSET
0,3
FORMULA
Apparent g.f.: (-b-sqrt(b^2-4*a*c))/(2*a) where a=(6*x^2 - 2*x), b=(-3*x^2 + 4*x - 1), and c=(-x + 1). [determined with Pari's seralgdep()]
Conjecture: D-finite with recurrence +(n+1)*a(n) +3*(-1)*a(n-1) +(-10*n+11)*a(n-2) +3*a(n-3) +9*(n-4)*a(n-4)=0. - R. J. Mathar, Mar 25 2024
MAPLE
A368773 := proc(n)
add(A059450(n-j, j), j=0..floor(n/2)) ;
end proc:
seq(A368773(n), n=0..40) ; # R. J. Mathar, Mar 25 2024
PROG
(PARI)
N=32; M=matrix(N+1, N+1); M[1, 1] = 1;
T(n, k)= return( M[n+1, k+1] );
{ \\ A059450
for (n=1, N,
for (k=0, n,
v = sum(y=0, n-1, T(y, k) ); \\ vert sum from top
h = sum(y=0, n-1, T(n, y) ); \\ horiz sum from left
s = v + h;
M[ n+1, k+1 ] = s;
);
); }
\\ antidiagonal sums:
for (n=0, N, my(r=n, c=0, s=0); while( c<=r, s+=T(r, c); r-=1; c+=1 ); print1(s, ", "));
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt, Jan 05 2024
STATUS
approved