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A048918 9-gonal hexagonal numbers. 3
1, 325, 5330229625, 1353857339341, 22184715227362706161, 5634830324997758086741, 92334031424171069457850940521, 23452480456295952079681300143325, 384299427405961840930468013697980089825, 97610541547790513644729906482502335077221 (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
Eric Weisstein's World of Mathematics, Nonagonal Hexagonal Number.
Index entries for linear recurrences with constant coefficients, signature (1,4162056194,-4162056194,-1,1).
FORMULA
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 *)
PROG
(PARI) Vec(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)) + O(x^20)) \\ Colin Barker, Jun 22 2015
CROSSREFS
Sequence in context: A048909 A097739 A203188 * A274307 A358148 A031516
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified February 27 08:19 EST 2024. Contains 370367 sequences. (Running on oeis4.)