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A124099
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Sum(x^i*y^j*z^k) with i + j + k = m and (x, y, z) = the primitive pythagorean triple (5, 12, 13).
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0
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1, 30, 619, 10920, 177061, 2726130, 40547359, 588485820, 8387148121, 117876868230, 1638536364499, 22574666496720, 308755233696781, 4197234089634330, 56765041887676039, 764357559726523620
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OFFSET
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0,2
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REFERENCES
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G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 196.
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LINKS
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Table of n, a(n) for n=0..15.
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FORMULA
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a(m) = (x^(m+2)*(z-y)+y^(m+2)*(x-z)+z^(m+2)*(y-x))/((x-y)*(y-z)*(z-x)).
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EXAMPLE
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a(2)=619 because sum(x^i*y^j*z^k)=x^2+y^2+z^2+x*y+x*z+y*z = 5^2+12^2+13^2+5*12+5*13+12*13 =619 and x^2+y^2=z^2
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MAPLE
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seq(sum(5^(m-n)*sum(12^p*13^(n-p), p=0..n), n=0..m), m=0..N);
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CROSSREFS
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Cf. A025942, A020000, A021664, A019682, A021684, A021844, A020340-A020342, A020344-A020346, A077515.
Sequence in context: A020980 A051303 A020975 * A028258 A075911 A001719
Adjacent sequences: A124096 A124097 A124098 * A124100 A124101 A124102
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KEYWORD
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nonn
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AUTHOR
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Giorgio Balzarotti and Paolo P. Lava, Nov 26 2006
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STATUS
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approved
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