A124100 Sum_(x^i*y^j*z^k) with i + j + k = m and (x, y, z) = the primitive Pythagorean triple (8, 15, 17).

1, 40, 1089, 25160, 531521, 10625640, 204744769, 3844391560, 70827391041, 1286290883240, 23101397290049, 411249127989960, 7269184506192961, 127745926316548840, 2234231991096868929, 38920247688751940360

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 (40, -511, 2040).

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) = 40*a(n-1) - 511*a(n-2) + 2040*a(n-3) for n > 2.

G.f.: 1/((1 - 8*x)*(1 - 15*x)*(1 - 17*x)). (End)

a(n) = 2^(3*n+6)/63 - 15^(n+2)/14 + 17^(n+2)/18. - Vaclav Kotesovec, Sep 25 2016

Example

a(2) = 1089 because x^2 + y^2 + z^2 + x*y + x*z + y*z = 8^2 + 15^2 + 17^2 + 8*15 + 8*17 + 15*17 = 1089 and x^2 + y^2 = z^2.

Maple

seq(sum(8^(m-n)*sum(15^p*17^(n-p), p=0..n), n=0..m), m=0..N);

Crossrefs

Cf. A019682, A020000, A020340-A020342, A020344-A020346, A021664, A021684, A021844, A025942, A077515.

Sequence in context: A075907 A062143 A284838 * A071952 A331906 A144914

Adjacent sequences: A124097 A124098 A124099 * A124101 A124102 A124103

Keyword

nonn

Author

Giorgio Balzarotti and Paolo P. Lava, Nov 26 2006

Status

approved