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%I #29 Mar 02 2024 00:03:28
%S 1,10,35,140,645,3150,15655,78160,390665,1953170,9765675,48828180,
%T 244140685,1220703190,6103515695,30517578200,152587890705,
%U 762939453210,3814697265715,19073486328220,95367431640725,476837158203230
%N a(n) = 5^n + 5*n.
%H Vincenzo Librandi, <a href="/A221907/b221907.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-11,5).
%F G.f.: (1+3*x-24*x^2)/((1-x)^2*(1-5*x)).
%F a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3).
%F a(n) = A176916(n) - 1.
%F a(n) = 5*A362555(n) for n > 0. - _Hugo Pfoertner_, Mar 01 2024
%t Table[(5^n + 5 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 3 x - 24 x^2)/((1 - x)^2 (1 - 5 x)), {x, 0, 30}], x]
%t LinearRecurrence[{7,-11,5},{1,10,35},30] (* _Harvey P. Dale_, Jul 23 2013 *)
%o (Magma) [5^n + 5*n: n in [0..30]]; /* or */ I:=[1, 10, 35]; [n le 3 select I[n] else 7*Self(n-1)-11*Self(n-2)+5*Self(n-3): n in [1..30]];
%o (PARI) a(n)=5^n+5*n \\ _Charles R Greathouse IV_, Apr 18 2013
%Y Cf. A107585, A176916, A362555, A370557.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Mar 02 2013
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