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A368773
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Antidiagonal sums of A059450.
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1
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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MAPLE
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add(A059450(n-j, j), j=0..floor(n/2)) ;
end proc:
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PROG
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(PARI)
N=32; M=matrix(N+1, N+1); M[1, 1] = 1;
T(n, k)= return( M[n+1, k+1] );
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, ", "));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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