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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 A250065 A180769

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

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Last modified December 18 08:30 EST 2014. Contains 252114 sequences.