OFFSET
1,2
COMMENTS
As n increases, this sequence is approximately geometric with common ratio r = lim_{n->infinity} a(n)/a(n-1) = (2+sqrt(3))^4 = 97 + 56*sqrt(3). - Ant King, Dec 14 2011
LINKS
Colin Barker, Table of n, a(n) for n = 1..438
Eric Weisstein's World of Mathematics, Hexagonal Pentagonal Number.
Index entries for linear recurrences with constant coefficients, signature (195,-195,1).
FORMULA
From Warut Roonguthai, Jan 08 2001: (Start)
a(n) = 194*a(n-1) - a(n-2) - 48.
G.f.: x*(1-52*x+3*x^2)/((1-x)*(1-194*x+x^2)). (End)
From Ant King, Dec 14 2011: (Start)
a(n) = 195*a(n-1) - 195*a(n-2) + a(n-3).
a(n) = (1/24)*sqrt(3)*((sqrt(3)-1)*(2+sqrt(3))^(4n-2)+(sqrt(3)+1)* (2-sqrt(3))^(4n-2)+2*sqrt(3)).
a(n) = ceiling((1/24)*sqrt(3)*(sqrt(3)-1)*(2+sqrt(3))^(4n-2)).
(End)
a(n) = A276915(2n-1). - Daniel Poveda Parrilla, Dec 03 2016
MATHEMATICA
LinearRecurrence[{195, -195, 1}, {1, 143, 27693}, 11] (* Ant King, Dec 14 2011 *)
PROG
(PARI) Vec(-x*(3*x^2-52*x+1)/((x-1)*(x^2-194*x+1)) + O(x^20)) \\ Colin Barker, Jun 21 2015
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
STATUS
approved