OFFSET
1,1
COMMENTS
Inspired by A274579.
a(n+1) / a(n) goes to 49 + 20*sqrt(6) when n goes to infinity.
LINKS
Colin Barker, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (99,-99,1).
FORMULA
From Colin Barker, Jun 30 2016: (Start)
a(n) = 99*a(n-1)-99*a(n-2)+a(n-3) for n>3.
G.f.: 45*x / ((1-x)*(1-98*x+x^2)).
(End)
EXAMPLE
45 is a term because 2*45 + 1 = 91 and 3*45 + 1 = 136 are both triangular numbers.
PROG
(PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(3*n+1, 3);
(PARI) Vec(45*x/((1-x)*(1-98*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 30 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Altug Alkan, Jun 30 2016
EXTENSIONS
More terms from Colin Barker, Jun 30 2016
STATUS
approved