|
|
A048905
|
|
Indices of octagonal numbers which are also heptagonal.
|
|
3
|
|
|
1, 315, 151669, 73103983, 35235967977, 16983663460771, 8186090552123485, 3945678662460058839, 1901808929215196236753, 916667958203062126055947, 441832054044946729562729541, 212962133381706120587109582655
(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(5)+sqrt(6))^4 = 241+44*sqrt(30). - Ant King, Dec 30 2011
|
|
LINKS
|
|
|
FORMULA
|
G.f.: -x*(1-168*x+7*x^2) / ( (x-1)*(x^2-482*x+1) ). - R. J. Mathar, Dec 21 2011
a(n) = 482*a(n-1)-a(n-2)-160.
a(n) = 1/120*((2*sqrt(5)+5*sqrt(6))*(sqrt(5)+sqrt(6))^(4n-3)+ (2*sqrt(5)-5*sqrt(6))*(sqrt(5)-sqrt(6))^(4n-3)+40).
a(n) = ceiling(1/120*(2*sqrt(5)+5*sqrt(6))*(sqrt(5)+sqrt(6))^(4n-3)). (End)
|
|
MATHEMATICA
|
LinearRecurrence[{483, -483, 1}, {1, 315, 151669}, 20] (* Vincenzo Librandi, Dec 28 2011 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|