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%I #13 Sep 08 2022 08:45:10
%S 1,5,37,257,1801,12605,88237,617657,4323601,30265205,211856437,
%T 1482995057,10380965401,72666757805,508667304637,3560671132457,
%U 24924697927201,174472885490405,1221310198432837,8549171389029857
%N a(n) = (3*7^n+(-1)^n)/4.
%C Binomial transform of A053524 (without leading zero).
%H Vincenzo Librandi, <a href="/A083232/b083232.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,7).
%F a(n) = (3*7^n+(-1)^n)/4.
%F G.f.: (1-x)/((1-7*x)*(1+x)).
%F E.g.f.: (3*exp(7*x)+exp(-x))/4
%o (Magma) [(3*7^n+(-1)^n)/4: n in [0..25]]; // _Vincenzo Librandi_, Jun 29 2011
%o (PARI) Vec((1-x)/((1-7*x)*(1+x)) + O(x^40)) \\ _Andrew Howroyd_, Feb 16 2018
%Y Cf. A083233.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Apr 23 2003