OFFSET
1,2
COMMENTS
Also positive integers x in the solutions to 3*x^2-5*y^2-x+5*y-2 = 0, the corresponding values of y being A253470.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (9,-9,1).
FORMULA
a(n) = 9*a(n-1)-9*a(n-2)+a(n-3).
G.f.: -x*(x^2-3*x+1) / ((x-1)*(x^2-8*x+1)).
a(n) = (2-(-5+sqrt(15))*(4+sqrt(15))^n+(4-sqrt(15))^n*(5+sqrt(15)))/12. - Colin Barker, Mar 03 2016
EXAMPLE
6 is in the sequence because the 6th pentagonal number is 51, which is also the 5th centered pentagonal number.
MATHEMATICA
LinearRecurrence[{9, -9, 1}, {1, 6, 46}, 30] (* Harvey P. Dale, Nov 12 2017 *)
PROG
(PARI) Vec(-x*(x^2-3*x+1)/((x-1)*(x^2-8*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 07 2015
STATUS
approved