OFFSET
1,2
COMMENTS
From Ant King, Oct 31 2011: (Start)
Limit_{n->oo} a(2*n+1)/a(2*n) = (6937 + 2832*sqrt(6))/25.
Limit_{n->oo} a(2*n)/a(2*n-1) = (217 + 88*sqrt(6))/25. (End)
REFERENCES
Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 39.
LINKS
Colin Barker, Table of n, a(n) for n = 1..500
Eric Weisstein's World of Mathematics, Octagonal Triangular Number.
Index entries for linear recurrences with constant coefficients, signature (1,9602,-9602,-1,1).
FORMULA
a(n+1) = 4801*a(n) + 1100 + 980*sqrt(24*a(n)^2+11*a(n)+1).
G.f.: -z*(z^4+20*z^3+2158*z^2+20*z+1) / ((z-1)*(z^2-98*z+1)*(z^2+98*z+1)). - Richard Choulet, Oct 03 2007, factored by Colin Barker, Feb 07 2015
From Ant King, Oct 31 2011: (Start)
a(n) = a(n-1) + 9602*a(n-2) - 9602*a(n-3) - a(n-4) + a(n-5).
a(n) = 9602*a(n-2) - a(n-4) + 2200.
a(n) = 1/96*((7-2*sqrt(6)*(-1)^n)*(sqrt(3)+sqrt(2))^(4*n-2)+(7+2*sqrt(6)*(-1)^n)*(sqrt(3)-sqrt(2))^(4*n-2)-22).
a(n) = floor(1/96*(7-2*sqrt(6)*(-1)^n)*(sqrt(3)+sqrt(2))^(4n-2)).
(End)
MATHEMATICA
LinearRecurrence[{1, 9602, -9602, -1, 1}, {1, 21, 11781, 203841, 113123361}, 13] (* Ant King, Oct 31 2011 *)
PROG
(PARI) Vec(-z*(z^4+20*z^3+2158*z^2+20*z+1)/((z-1)*(z^2-98*z+1)*(z^2+98*z+1)) + O(z^36)) \\ Joerg Arndt, Feb 07 2015, factored by Colin Barker, Feb 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Richard Choulet, Oct 03 2007
STATUS
approved