OFFSET
1,2
COMMENTS
As n increases, this sequence is approximately geometric with common ratio r = lim_{n->infinity} a(n)/a(n-1) = (4+sqrt(15))^2 = 31 + 8*sqrt(15). - Ant King, Dec 15 2011
LINKS
Colin Barker, Table of n, a(n) for n = 1..558
Eric Weisstein's World of Mathematics, Heptagonal Pentagonal Number.
Index entries for linear recurrences with constant coefficients, signature (63,-63,1)
FORMULA
From Ant King, Dec 15 2011: (Start)
a(n) = 63*a(n-1) - 63*a(n-2) + a(n-3).
a(n) = 62*a(n-1) - a(n-2) - 18.
a(n) = (1/60)*((9-sqrt(15))*(4+sqrt(15))^(2*n-1) + (9+sqrt(15))*(4-sqrt(15))^(2*n-1)+18).
a(n) = ceiling((1/60)*(9-sqrt(15))*(4+sqrt(15))^(2*n-1)).
G.f.: x*(1-21*x+2*x^2)/((1-x)*(1-62*x+x^2)).
(End)
MATHEMATICA
LinearRecurrence[{63, -63, 1}, {1, 42, 2585}, 14] (* Ant King, Dec 15 2011 *)
PROG
(PARI) Vec(-x*(2*x^2-21*x+1)/((x-1)*(x^2-62*x+1)) + O(x^30)) \\ Colin Barker, Jun 23 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved