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a(n) = (3*7^n+(-1)^n)/4.
3

%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