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%I #13 Aug 01 2015 10:03:39
%S 1,551,494461,444025091,398734036921,358062721129631,
%T 321539924840371381,288742494443932370171,259290438470726428041841,
%U 232842525004217888449202711,209092328163349193100955992301,187764677848162571186770031883251
%N Indices of 10-gonal (decagonal) numbers which are also 9-gonal (nonagonal).
%C As n increases, this sequence is approximately geometric with common ratio r = lim(n->Infinity, a(n)/a(n-1)) = (2*sqrt(2)+sqrt(7))^4 = 449+120*sqrt(14).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (899, -899, 1).
%F G.f.: x*(1-348*x+11*x^2) / ((1-x)*(1-898*x+x^2)).
%F a(n) = 898*a(n-1)-a(n-2)-336.
%F a(n) = 899*a(n-1)-899*a(n-2)+a(n-3).
%F a(n) = 1/112*((sqrt(7)+7*sqrt(2))*(2*sqrt(2)+sqrt(7))^(4*n-3)-(sqrt(7)-7*sqrt(2))*(2*sqrt(2)-sqrt(7))^(4*n-3)+42).
%F a(n) = ceiling(1/112*(sqrt(7)+7*sqrt(2))*(2*sqrt(2)+sqrt(7))^(4*n-3)).
%e The second number that is both 9-gonal (nonagonal) and 10-gonal (decagonal) is A001107(551) = 1212751. Hence a(2) = 551.
%t LinearRecurrence[{899, -899, 1}, {1, 551, 494461}, 12]
%Y Cf. A203627, A203628, A001107, A001106.
%K nonn,easy
%O 1,2
%A _Ant King_, Jan 06 2012
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