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%I #25 Sep 08 2022 08:44:48
%S 1,4,23,122,621,3120,15619,78118,390617,1953116,9765615,48828114,
%T 244140613,1220703112,6103515611,30517578110,152587890609,
%U 762939453108,3814697265607,19073486328106,95367431640605
%N a(n) = 5^n - n.
%H Vincenzo Librandi, <a href="/A024050/b024050.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-11,5).
%F a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3).
%F G.f.: (1 - 3*x + 6*x^2)/((1-5*x)*(1-x)^2). - _Vincenzo Librandi_, Jun 16 2013
%p g:=1/(1-5*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)-n, n=0..31); # _Zerinvary Lajos_, Jan 09 2009
%t Table[5^n - n, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 3 x + 6 x^2) / ((1 - 5 x) (1 - x)^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jun 16 2013 *)
%t LinearRecurrence[{7,-11,5},{1,4,23},30] (* _Harvey P. Dale_, Mar 03 2022 *)
%o (Magma) [5^n-n: n in [0..35]]; // _Vincenzo Librandi_, Jun 12 2011
%Y Cf. numbers of the form k^n-n: A000325 (k=2), A024024 (k=3), A024037 (k=4), this sequence (k=5), A024063 (k=6), A024076 (k=7), A024089 (k=8), A024102 (k=9), A024115 (k=10), A024128 (k=11), A024141 (k=12).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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