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a(n) = 5^n + 5*n + 1.
4

%I #23 Aug 23 2024 20:54:43

%S 2,11,36,141,646,3151,15656,78161,390666,1953171,9765676,48828181,

%T 244140686,1220703191,6103515696,30517578201,152587890706,

%U 762939453211,3814697265716,19073486328221,95367431640726,476837158203231,2384185791015736,11920928955078241,59604644775390746

%N a(n) = 5^n + 5*n + 1.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-11,5).

%F a(n) = A000351(n) + A008587(n) + 1 = A000351(n) + A016861(n).

%F From _R. J. Mathar_, Apr 29 2010: (Start)

%F a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3).

%F G.f.: ( -2+3*x+19*x^2 ) / ( (5*x-1)*(x-1)^2 ). (End)

%F E.g.f.: exp(x)*(1 + exp(4*x) + 5*x). - _Stefano Spezia_, Aug 19 2024

%e a(3) = 5^3 + 5*3 + 1 = 141.

%t LinearRecurrence[{7,-11,5},{2,11,36},25] (* _Stefano Spezia_, Aug 19 2024 *)

%o (PARI) a(n)=5^n+5*n+1 \\ _Charles R Greathouse IV_, Aug 23 2024

%Y Cf. A000351, A008587, A016861, A176691, A176805.

%K nonn,easy

%O 0,1

%A _Jonathan Vos Post_, Apr 28 2010

%E First term corrected by several authors, Apr 29 2010

%E a(22)-a(24) from _Stefano Spezia_, Aug 19 2024