OFFSET
1,2
COMMENTS
Also positive integers x in the solutions to 3*x^2 - 8*y^2 - 3*x + 8*y = 0, the corresponding values of y being A253674.
Also indices of centered square numbers (A001844) that are also octagonal numbers (A000567). - Colin Barker, Feb 10 2015
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,98,-98,-1,1).
FORMULA
a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5).
G.f.: x*(3*x-1)*(5*x^2+18*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).
EXAMPLE
16 is in the sequence because the 16th centered triangular number is 361, which is also the 10th centered octagonal number.
MATHEMATICA
LinearRecurrence[{1, 98, -98, -1, 1}, {1, 16, 65, 1520, 6321}, 20] (* Harvey P. Dale, Aug 07 2023 *)
PROG
(PARI) Vec(x*(3*x-1)*(5*x^2+18*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 08 2015
STATUS
approved