OFFSET
0,2
REFERENCES
G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 196.
LINKS
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
KEYWORD
nonn
AUTHOR
Giorgio Balzarotti and Paolo P. Lava, Nov 26 2006
STATUS
approved