OFFSET
0,2
REFERENCES
G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 197.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..720
Index entries for linear recurrences with constant coefficients, signature (56,-943,4200).
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) = 56*a(n-1) - 943*a(n-2) + 4200*a(n-3) for n > 2.
G.f.: 1/((1 - 7*x)*(1 - 24*x)*(1 - 25*x)). (End)
a(n) = 5^(2*n+4)/18 + 7^(n+2)/306 - 2^(3*n+6)*3^(n+2)/17. - Vaclav Kotesovec, Sep 25 2016
EXAMPLE
a(2) = 2193 because x^2 + y^2 + z^2 + x*y + x*z + y*z = 7^2 + 24^2 + 25^2 + 7*24 + 7*25 + 24*25 = 2193 and x^2 + y^2 = z^2.
MAPLE
seq(sum(7^(m-n)*sum(24^p*25^(n-p), p=0..n), n=0..m), m=0..N);
MATHEMATICA
CoefficientList[Series[1/((1 - 7 x) (1 - 24 x) (1 - 25 x)), {x, 0, 15}], x] (* Michael De Vlieger, Sep 25 2016 *)
LinearRecurrence[{56, -943, 4200}, {1, 56, 2193}, 50] (* Vincenzo Librandi, Aug 18 2018 *)
PROG
(Magma) [5^(2*n+4)/18 + 7^(n+2)/306 - 2^(3*n+6)*3^(n+2)/17 : n in [0..20]]; // Wesley Ivan Hurt, Sep 26 2016
(PARI) x='x+O('x^99); Vec(1/((1-7*x)*(1-24*x)*(1-25*x))) \\ Altug Alkan, Sep 26 2016
(Magma) I:=[1, 56, 2193]; [n le 3 select I[n] else 56*Self(n-1)-943*Self(n-2)+4200*Self(n-3): n in [1..90]]; // Vincenzo Librandi, Aug 18 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Giorgio Balzarotti and Paolo P. Lava, Nov 26 2006
STATUS
approved