OFFSET
1,2
COMMENTS
Positive integers y in the solutions to 3*x^2 - 8*y^2 - x + 8*y - 2 = 0, the corresponding values of x beingA046172.
LINKS
Colin Barker,Table of n, a(n) for n = 1..503
Index entries for linear recurrences with constant coefficients,signature (99,-99,1).
FORMULA
a(n) = 99*a(n-1) - 99*a(n-2) + a(n-3).
G.f.: x*(49*x-1) / ((x-1)*(x^2 - 98*x + 1)).
a(n) = (1/2+1/48*(49+20*sqrt(6))^(-n)*(-12-5*sqrt(6)+(-12+5*sqrt(6))*(49+20*sqrt(6))^(2*n))). -Colin Barker,Mar 03 2016
EXAMPLE
50 is in the sequence because the 50th centered octagonal number is 9801, which is also the 81st pentagonal number.
MATHEMATICA
LinearRecurrence[{99, -99, 1}, {1, 50, 4851}, 20] (*Vincenzo Librandi,Jun 13 2015 *)
PROG
(PARI) Vec(x*(49*x-1)/((x-1)*(x^2-98*x+1)) + O(x^100))
(Magma) I:=[1, 50, 4851]; [n le 3 select I[n] else 99*Self(n-1)-99*Self(n-2)+Self(n-3): n in [1..20]]; //Vincenzo Librandi,Jun 13 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker,Jan 11 2015
STATUS
approved