OFFSET
1,2
COMMENTS
As n increases, this sequence is approximately geometric with common ratio r = lim_{n->oo} a(n)/a(n-1) = (4+sqrt(15))^4=1921+496*sqrt(15). - Ant King, Dec 15 2011
REFERENCES
Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 38.
LINKS
Colin Barker, Table of n, a(n) for n = 1..279
Eric Weisstein's World of Mathematics, Heptagonal Pentagonal Number.
Index entries for linear recurrences with constant coefficients, signature (3843,-3843,1).
FORMULA
From Ant King, Dec 15 2011: (Start)
a(n) = 3843*a(n-1) - 3843*a(n-2) + a(n-3).
a(n) = 3842*a(n-1) - a(n-2) + 512.
a(n) = 1/240*((2+sqrt(15))^2*(4+sqrt(15))^(4n-3)+ (2-sqrt(15))^2*(4-sqrt(15))^(4n-3)-32).
a(n) = floor(1/240*((2+sqrt(15))^2*(4+sqrt(15))^(4n-3))).
G.f.: x*(1+504*x+7*x^2)/((1-x)*(1-3842*x+x^2)). (End)
MATHEMATICA
LinearRecurrence[{3843, -3843, 1}, {1, 4347, 16701685}, 10] (* Ant King, Dec 15 2011 *)
PROG
(PARI) Vec(-x*(7*x^2+504*x+1)/((x-1)*(x^2-3842*x+1)) + O(x^30)) \\ Colin Barker, Jun 23 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved