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%I #28 Sep 10 2024 17:21:37
%S 1,14,63,364,2429,16842,117691,823592,5764857,40353670,282475319,
%T 1977326820,13841287285,96889010498,678223072947,4747561510048,
%U 33232930569713,232630513987326,1628413597910575,11398895185373276,79792266297612141,558545864083284154,3909821048582988203
%N a(n) = 7^n + 7*n.
%H Vincenzo Librandi, <a href="/A221909/b221909.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-15,7).
%F G.f.: (1+5*x-48*x^2)/((1-x)^2*(1-7*x)).
%F a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3).
%F a(n) = A176972(n) - 1.
%F E.g.f.: exp(x)*(exp(6*x) + 7*x). - _Elmo R. Oliveira_, Sep 10 2024
%t Table[(7^n + 7 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 5 x - 48 x^2)/((1 - x)^2 (1 - 7 x)), {x, 0, 30}], x]
%o (Magma) [7^n + 7*n: n in [0..30]]; /* or */ I:=[1, 14, 63]; [n le 3 select I[n] else 9*Self(n-1)-15*Self(n-2)+7*Self(n-3): n in [1..30]];
%o (PARI) a(n)=7^n+7*n \\ _Charles R Greathouse IV_, Apr 18 2013
%Y Cf. A176972, A198397.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Mar 02 2013