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A046183
Octagonal triangular numbers.
3
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
Eric Weisstein's World of Mathematics, Octagonal Triangular Number.
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
Sequence in context: A013726 A159358 A048914 * A203674 A250065 A180769
KEYWORD
nonn,easy
EXTENSIONS
More terms from Richard Choulet, Oct 03 2007
STATUS
approved