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A124099 Sum_(x^i*y^j*z^k) with i + j + k = m and (x, y, z) = the primitive Pythagorean triple (5, 12, 13). 0
1, 30, 619, 10920, 177061, 2726130, 40547359, 588485820, 8387148121, 117876868230, 1638536364499, 22574666496720, 308755233696781, 4197234089634330, 56765041887676039, 764357559726523620 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 196.

LINKS

Table of n, a(n) for n=0..15.

FORMULA

a(m) = (x^(m+2)*(z-y)+y^(m+2)*(x-z)+z^(m+2)*(y-x))/((x-y)*(y-z)*(z-x)).

From Chai Wah Wu, Sep 24 2016: (Start)

a(n) = 30*a(n-1) - 281*a(n-2) + 780*a(n-3) for n > 2.

G.f.: 1/((1 - 5*x)*(1 - 12*x)*(1 - 13*x)). (End)

EXAMPLE

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.

MAPLE

seq(sum(5^(m-n)*sum(12^p*13^(n-p), p=0..n), n=0..m), m=0..N);

CROSSREFS

Cf. A019682, A020000, A020341, A020346, A021664, A021684, A021844, A025942.

Sequence in context: A020975 A277877 A279870 * A028258 A285235 A075911

Adjacent sequences:  A124096 A124097 A124098 * A124100 A124101 A124102

KEYWORD

nonn

AUTHOR

Giorgio Balzarotti and Paolo P. Lava, Nov 26 2006

STATUS

approved

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Last modified May 28 04:36 EDT 2020. Contains 334671 sequences. (Running on oeis4.)