A368773 Antidiagonal sums of A059450.

1, 1, 3, 7, 21, 53, 159, 419, 1257, 3401, 10203, 28095, 84285, 235005, 705015, 1984155, 5952465, 16873745, 50621235, 144327287, 432981861, 1240296773, 3720890319, 10700364691, 32101094073, 92619680089, 277859040267, 803956981807, 2411870945421, 6995553520653, 20986660561959, 61001041404555

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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

Cf. A059450.

Sequence in context: A018303 A098545 A161707 * A192068 A368098 A318395

Adjacent sequences: A368770 A368771 A368772 * A368774 A368775 A368776

Keyword

nonn

Author

Joerg Arndt, Jan 05 2024

Status

approved