|
| |
|
|
A046183
|
|
Octagonal triangular numbers.
|
|
2
|
|
|
|
1, 21, 11781, 203841, 113123361, 1957283461, 1086210502741, 18793835590881, 10429793134197921, 180458407386358101, 100146872588357936901, 1732761608929974897121, 961610260163619775927681
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
From Ant King, Oct 31 2011: (Start)
limit n -> infinity, u(2n+1)/u(2n)) = 1/25*(6937+2832*sqrt(6)).
limit n -> infinity, u(2n)/u(2n-1)) = 1/25*(217+88*sqrt(6)).
(End)
|
|
|
LINKS
|
Table of n, a(n) for n=1..13.
Eric Weisstein's World of Mathematics, Octagonal Triangular Number.
Index to sequences with 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+21*z^2+2178*z^3+2178*z^4+21*z^5+z^6)/((1-z^2)*(1-9602*z^2+z^4)) (the numerator is divisible by 1+z but it is more "symmetric" like that) - Richard Choulet, Oct 03 2007
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 *)
|
|
|
CROSSREFS
|
Cf. A046181, A046182.
Sequence in context: A013726 A159358 A048914 * A203674 A180769 A220643
Adjacent sequences: A046180 A046181 A046182 * A046184 A046185 A046186
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Eric W. Weisstein
|
|
|
EXTENSIONS
|
More terms from Richard Choulet, Oct 03 2007
|
|
|
STATUS
|
approved
|
| |
|
|
