|
| |
|
|
A046181
|
|
Indices of octagonal numbers which are also triangular.
|
|
2
| |
|
|
1, 3, 63, 261, 6141, 25543, 601723, 2502921, 58962681, 245260683, 5777740983, 24033043981, 566159653621, 2354993049423, 55477868313843, 230765285799441, 5436264935102961, 22612643015295763
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| From Ant King, Nov 1 2011: (Start)
limit n -> infinity, a(2n+1)/a(2n)) = 1/5*(59+24*sqrt(6)).
limit n -> infinity, a(2n)/a(2n-1)) = 1/5*(11+4*sqrt(6)).
(End)
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Octagonal Triangular Number
|
|
|
FORMULA
| For n odd, a(n+2)=98*a(n+1)-a(n)-32; for n even, a(n+1)=49*a(n)-16+10*(24*a(n)^2-16*a(n)+1)^0.5 - Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 03 2007, Oct 09 2007
From Ant King, Nov 1 2011: (Start)
a(n) = a(n-1) + 98*a(n-2) - 98*a(n-3) - a(n-4) + a(n-5).
a(n) = 98*a(n-2) - a(n-4) - 32.
a(n) = 1/24*sqrt(2)(( sqrt(6)-(-1)^n)*(sqrt(3)+sqrt(2))^(2*n-1)+(sqrt(6)+(-1)^n)*(sqrt(3)-sqrt(2))^(2*n-1)+4*sqrt(2)).
a(n) = ceiling(1/24* sqrt(2)*(sqrt(6)-(-1)^n)*(sqrt(3)+sqrt(2))^(2*n-1)).
Gf: x(1+2*x-38*x^2+2*x^3+x^4)/((1-x)(1-10*x+x^2)(1+10*x+x^2)).
(End)
|
|
|
MATHEMATICA
| LinearRecurrence[{1, 98, -98, -1, 1}, {1, 3, 63, 261, 6141}, 18] (* Ant King, Nov 01 2011 *)
|
|
|
CROSSREFS
| Cf. A046182, A046183.
Sequence in context: A087886 A123754 A048354 * A151993 A120053 A139293
Adjacent sequences: A046178 A046179 A046180 * A046182 A046183 A046184
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
|
|
|
EXTENSIONS
| More terms from Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 03 2007
|
| |
|
|
