A124099 Sum_(x^i*y^j*z^k) with i + j + k = m and (x, y, z) = the primitive Pythagorean triple (5, 12, 13).

1, 30, 619, 10920, 177061, 2726130, 40547359, 588485820, 8387148121, 117876868230, 1638536364499, 22574666496720, 308755233696781, 4197234089634330, 56765041887676039, 764357559726523620

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.

Index entries for linear recurrences with constant coefficients, signature (30, -281, 780).

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