|
|
A048907
|
|
Indices of 9-gonal numbers which are also triangular.
|
|
4
|
|
|
1, 10, 154, 2449, 39025, 621946, 9912106, 157971745, 2517635809, 40124201194, 639469583290, 10191389131441, 162422756519761, 2588572715184730, 41254740686435914, 657487278267789889, 10478541711598202305, 166999180107303446986, 2661508340005256949466
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
lim(n -> Infinity, a(n)/a(n-1)) = 8 + 3*sqrt(7). - Ant King, Nov 03 2011
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(1-7*x+x^2)/((1-x)*(1-16*x+x^2)).
a(n+2) = 16*a(n+1)-a(n)-5, a(n+1) = 8*a(n)-2.5+1.5*(28*a(n)^2-20*a(n)+1)^0.5. - Richard Choulet, Sep 22 2007
a(n) = 17*a(n-1) - 17*a(n-2) + a(n-3).
a(n) = ceiling(3/28*(3-sqrt(7))*(8 + 3*sqrt(7))^n).
(End)
|
|
MATHEMATICA
|
LinearRecurrence[{17, -17, 1}, {1, 10, 154}, 17]; (* Ant King, Nov 03 2011 *)
|
|
PROG
|
(PARI) Vec(-x*(x^2-7*x+1)/((x-1)*(x^2-16*x+1)) + O(x^20)) \\ Colin Barker, Jun 22 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|