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%I #24 Aug 16 2015 12:03:56
%S 1,121771,12625478965,1309034909945503,135723357520344181225,
%T 14072069153115290487843091,1459020273797576190840203197981,
%U 151274140013808225465578657485241095,15684405383452644158924550174544564031953,1626190518815862911671806985731550830475727995
%N Heptagonal hexagonal numbers.
%C As n increases, this sequence is approximately geometric with common ratio r = lim(n->Infinity,a(n)/a(n-1)) = (2+sqrt(5))^8 = 51841+23184*sqrt(5). - _Ant King_, Dec 24 2011
%H Colin Barker, <a href="/A048903/b048903.txt">Table of n, a(n) for n = 1..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeptagonalHexagonalNumber.html">Heptagonal Hexagonal Number</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (103683,-103683,1).
%F From _Ant King_, Dec 24 2011: (Start)
%F G.f.: x*(1+18088*x+55*x^2)/((1-x)*(1-103682*x+x^2)).
%F a(n) = 103683*a(n-1)-103683*a(n-2)+a(n-3).
%F a(n) = 103682*a(n-1)-a(n-2)+18144.
%F a(n) = 1/80*((sqrt(5)-1)*(2+sqrt(5))^(8n-5)- (sqrt(5)+1)*(2-sqrt(5))^(8n-5)-14).
%F a(n) = floor(1/80*(sqrt(5)-1)*(2+sqrt(5))^(8n-5)).
%F (End)
%t LinearRecurrence[{103683, -103683, 1}, {1, 121771, 12625478965}, 8]; (* _Ant King_, Dec 24 2011 *)
%o (PARI) Vec(-x*(55*x^2+18088*x+1)/((x-1)*(x^2-103682*x+1)) + O(x^20)) \\ _Colin Barker_, Jun 23 2015
%Y Cf. A048901, A048902.
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_
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