|
| |
|
|
A048918
|
|
9-gonal hexagonal numbers.
|
|
2
|
| |
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
As n increases, the ratio of consecutive terms forms an approximate 2-cycle with the ratio a(n)/a(n-1) bounded above and below by 8193151+3096720*sqrt(7) and 127+48*sqrt(7) respectively. - Ant King, Dec 27 2011
|
|
|
LINKS
|
Table of n, a(n) for n=1..8.
Eric Weisstein's World of Mathematics, Nonagonal Hexagonal Number.
Index to sequences with linear recurrences with constant coefficients, signature (1,4162056194,-4162056194,-1,1).
|
|
|
FORMULA
|
Contribution from Ant King, Dec 28 2011: (Start)
G.f.: x*(1+324*x+1168173106*x^2+20902860*x^3+82621*x^4) / ((1-x)*(1-64514*x+x^2)*(1+64514*x+x^2)).
a(n) = 4162056194*a(n-2)-a(n-4)+1189158912.
a(n) = a(n-1)+4162056194*a(n-2)-4162056194*a(n-3)-a(n-4)+a(n-5).
a(n) = 1/112*(9*((8-3*sqrt(7)*(-1)^n)*(8+3*sqrt(7))^(4*n-4)+(8+3*sqrt(7)*(-1)^n)*(8-3*sqrt(7))^(4*n-4))-32).
a(n) = floor(9/112*(8-3*sqrt(7)*(-1)^n)*(8+3*sqrt(7))^(4*n-4)).
(End)
|
|
|
MATHEMATICA
|
LinearRecurrence[{1, 4162056194, -4162056194, -1, 1}, {1, 325, 5330229625, 1353857339341, 22184715227362706161}, 8] (* Ant King, Dec 27 2011 *)
|
|
|
CROSSREFS
|
Cf. A048916, A048917.
Sequence in context: A048909 A097739 A203188 * A031516 A066128 A138816
Adjacent sequences: A048915 A048916 A048917 * A048919 A048920 A048921
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Eric W. Weisstein
|
|
|
STATUS
|
approved
|
| |
|
|
