OFFSET
1,1
COMMENTS
For the first of the corresponding three consecutive positive integers, see A261973.
LINKS
Colin Barker, Table of n, a(n) for n = 1..601
Index entries for linear recurrences with constant coefficients, signature (47,-47,1).
FORMULA
a(n) = 47*a(n-1)-47*a(n-2)+a(n-3) for n>3.
G.f.: x*(5*x^2-158*x-67) / ((x-1)*(x^2-46*x+1)).
a(n) = -5+3*sqrt(3/11)*(23+4*sqrt(33))^(-n)*(-1+(23+4*sqrt(33))^(2*n)). - Colin Barker, Mar 03 2016
EXAMPLE
67 is in the sequence because 67^2 + ... + 77^2 = 57134 = 137^2 + 138^2 + 139^2.
MATHEMATICA
LinearRecurrence[{47, -47, 1}, {67, 3307, 152275}, 20] (* Harvey P. Dale, Jul 02 2016 *)
PROG
(PARI) Vec(x*(5*x^2-158*x-67)/((x-1)*(x^2-46*x+1)) + O(x^40))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Sep 07 2015
STATUS
approved