OFFSET
1,2
COMMENTS
Also positive integers y in the solutions to x^2 - 8*y^2 + x + 8*y - 2 = 0, the corresponding values of x being A008843.
Also the indices of centered octagonal numbers (A016754) which are also hexagonal numbers (A000384). Also positive numbers y in the solutions to 4x^2-8y^2-2x+8y-2=0. - Colin Barker, Jan 25 2015
LINKS
Colin Barker, Table of n, a(n) for n = 1..654
Index entries for linear recurrences with constant coefficients, signature (35,-35,1).
FORMULA
a(n) = 35*a(n-1)-35*a(n-2)+a(n-3).
G.f.: x*(17*x-1) / ((x-1)*(x^2-34*x+1)).
a(n) = sqrt((-2-(17-12*sqrt(2))^n-(17+12*sqrt(2))^n)*(2-(17-12*sqrt(2))^(1+n)-(17+12*sqrt(2))^(1+n)))/(8*sqrt(2)). - Gerry Martens, Jun 04 2015
EXAMPLE
18 is in the sequence because the 18th centered octagonal number is 1225, which is also the 49th triangular number.
18 is in the sequence because the 18th centered octagonal number 1225 is also the 25th hexagonal number. - Colin Barker, Jan 25 2015
PROG
(PARI) Vec(x*(17*x-1)/((x-1)*(x^2-34*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 16 2015
STATUS
approved