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A048918 9-gonal hexagonal numbers. 2
1, 325, 5330229625, 1353857339341, 22184715227362706161, 5634830324997758086741, 92334031424171069457850940521, 23452480456295952079681300143325 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 22 20:13 EST 2014. Contains 249827 sequences.