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A137280 a(n) = 3*a(n-1) + 7*a(n-2), with a(1) = 1, a(2) = 10.

%I A137280 #21 Jan 15 2025 10:23:55
%S A137280 1,10,37,181,802,3673,16633,75610,343261,1559053,7079986,32153329,
%T A137280 146019889,663132970,3011538133,13676545189,62110402498,282067023817,
%U A137280 1280973888937,5817390833530,26418989723149,119978705004157,544869043074514,2474458064252641,11237457494279521
%N A137280 a(n) = 3*a(n-1) + 7*a(n-2), with a(1) = 1, a(2) = 10.
%C A137280 a(n) == 1 mod 9.
%C A137280 a(n)/a(n-1) tends to 4.54138126... = (3 + sqrt(37))/2.
%H A137280 Andrew Howroyd, <a href="/A137280/b137280.txt">Table of n, a(n) for n = 1..500</a>
%H A137280 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,7)
%F A137280 a(1) = 1, a(2) = 10, a(n) = 3*a(n-1) + 7*a(n-2) for n>2.
%F A137280 a(n) = upper left term in [1,3; 3,2]^n
%F A137280 From _R. J. Mathar_, Mar 17 2008: (Start)
%F A137280 O.g.f.: x*(1+7*x)/(1-3*x-7*x^2).
%F A137280 a(n) = A015524(n) + 7*A015524(n-1). (End)
%e A137280 a(4) = 181 = 3*a(3) + 7*a(2) = 3*37 + 7*10.
%e A137280 a(4) = 181 = upper left term in [1,3; 3,2]^4.
%t A137280 LinearRecurrence[{3, 7}, {1, 10}, 25] (* _Paolo Xausa_, Jan 15 2025 *)
%K A137280 nonn,easy
%O A137280 1,2
%A A137280 _Gary W. Adamson_, Mar 14 2008
%E A137280 a(23) onwards from _Andrew Howroyd_, Jan 12 2025