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A294159
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Alternating row sums of triangle A291844.
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3
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1, 1, 2, 6, 18, 55, 171, 538, 1708, 5461, 17560, 56728, 183973, 598597, 1953145, 6388376, 20939664, 68764283, 226192964, 745146462, 2458020664, 8118111977, 26841209903, 88835163150, 294284206183, 975699571009, 3237456793478, 10749922312752, 35718863630895, 118757413662397
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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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G.f. y(x) satisfies: 0 = (x^3 + x^2 + 3*x - 1)*(y^2 - y) + x.
Conjecture: D-finite with recurrence n*a(n) +(-3*n+1)*a(n-1) +2*(-n+3)*a(n-2) +2*(n-5)*a(n-3) +(n-4)*a(n-4) +(n-5)*a(n-5)=0. - R. J. Mathar, Jun 17 2020
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PROG
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(PARI)
my(x='x+O('x^N), y=1, y1=0, n=1,
dn = 1/(-2*t^2*x^4 - (2*t^2+3*t)*x^3 - (2*t+1)*x^2 + (2*t-1)*x + 1));
while (n++,
y1 = (2*x^2*y'*((-t^2 + t)*x + (-t + 1) + (t^2*x^2 + (t^2 + t)*x + t)*y) +
(t*x^2 + t*x)*y^2 - (2*t^2*x^3 + 3*t*x^2 + (-t + 1)*x - 1))*dn;
if (y1 == y, break); y = y1; ); y;
};
((1+x)*z - 1)*(1 + t*x)/((1-t + t*(1+x)*z)*x*z^2);
};
\\ test: y=A291844_ser(200, -1); 0==(x^3 + x^2 + 3*x - 1)*(y^2 - y) + x
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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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