OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..450
Index entries for linear recurrences with constant coefficients, signature (111,-111,1).
FORMULA
a(n+2) = 110*a(n+1) - a(n) + 378.
G.f.: 7*x*(-1-55*x+2*x^2) / ( (x-1)*(x^2-110*x+1) ). - R. J. Mathar, Nov 27 2011
a(n) = 7*A144929(n). - R. J. Mathar, Nov 27 2011
EXAMPLE
a(1)=7 because 14^3-7^3=49^2.
MATHEMATICA
Last /@ Table[n /. {ToRules[Reduce[n > 0 && k >= 0 && (n + 7)^3 - n^3 == k^2, n, Integers] /. C[1] -> c]} // Simplify, {c, 1, 14}] (* or *)
Rest@ CoefficientList[Series[7 x (-1 - 55 x + 2 x^2)/((x - 1) (x^2 - 110 x + 1)), {x, 0, 14}], x] (* Michael De Vlieger, Jul 14 2016 *)
LinearRecurrence[{111, -111, 1}, {7, 1162, 128191}, 20] (* Harvey P. Dale, Jul 05 2024 *)
PROG
(PARI) Vec(7*x*(-1-55*x+2*x^2)/((x-1)*(x^2-110*x+1)) + O(x^20)) \\ Colin Barker, Jul 14 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Sep 25 2008
STATUS
approved