|
|
A048923
|
|
Indices of octagonal numbers which are also 9-gonal.
|
|
3
|
|
|
1, 459, 309141, 208360351, 140434567209, 94652689938291, 63795772583840701, 42998256068818693959, 28980760794611215887441, 19532989777311890689441051, 13165206129147419713467380709
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
As n increases, this sequence is approximately geometric with common ratio r = lim_{n->infinity} a(n)/a(n-1) = (sqrt(6) + sqrt(7))^4 = 337 + 52*sqrt(42). - Ant King, Jan 03 2012
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(-1 + 216*x + 9*x^2) / ( (x-1)*(x^2 - 674*x + 1) ). - R. J. Mathar, Dec 21 2011
a(n) = 674*a(n-1) - a(n-2) - 224.
a(n) = (1/168)*((7*sqrt(6) + 2*sqrt(7))*(sqrt(6) + sqrt(7))^(4*n-3) + (7*sqrt(6) - 2*sqrt(7))*(sqrt(6) - sqrt(7))^(4*n-3) + 56).
a(n) = ceiling((1/168)*(7*sqrt(6) + 2*sqrt(7))*(sqrt(6) + sqrt(7))^(4*n-3)). (End)
|
|
MATHEMATICA
|
LinearRecurrence[{675, -675, 1}, {1, 459, 309141}, 30] (* Vincenzo Librandi, Dec 24 2011 *)
|
|
PROG
|
(Magma) I:=[1, 459, 309141]; [n le 3 select I[n] else 675*Self(n-1)-675*Self(n-2)+Self(n-3): n in [1..15]]; // Vincenzo Librandi, Dec 24 2011
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|