A046183 Octagonal triangular numbers.

1, 21, 11781, 203841, 113123361, 1957283461, 1086210502741, 18793835590881, 10429793134197921, 180458407386358101, 100146872588357936901, 1732761608929974897121, 961610260163619775927681, 16637976788487211575799941, 9233381617944204500099658261, 159757851390292596620856138561

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)

Intersection of A000217 and A000567. - Michel Marcus, Feb 07 2015

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

Cf. A046181, A046182.

Sequence in context: A013726 A159358 A048914 * A203674 A250065 A180769

Adjacent sequences: A046180 A046181 A046182 * A046184 A046185 A046186

Keyword

nonn,easy

Author

Eric W. Weisstein

Extensions

More terms from Richard Choulet, Oct 03 2007

Status

approved