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 A013915 a(n) = F(n) + L(n) + n, where F(n) (A000045) and L(n) (A000204) are Fibonacci and Lucas numbers respectively. 1

%I

%S 3,3,7,10,16,24,37,57,89,140,222,354,567,911,1467,2366,3820,6172,9977,

%T 16133,26093,42208,68282,110470,178731,289179,467887,757042,1224904,

%U 1981920,3206797,5188689,8395457,13584116,21979542,35563626,57543135

%N a(n) = F(n) + L(n) + n, where F(n) (A000045) and L(n) (A000204) are Fibonacci and Lucas numbers respectively.

%H Vincenzo Librandi, <a href="/A013915/b013915.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, -1, 1).

%F a(n) = a(n-1) + a(n-2) - n + 3.

%F From _R. J. Mathar_, Nov 04 2009: (Start)

%F a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4).

%F G.f.: (-3 + 6*x - 4*x^2 + 2*x^3)/((x^2+x-1) * (x-1)^2).

%F a(n) = n + A013655(n). (End)

%t LinearRecurrence[{3,-2,-1, 1},{3,3,7,10},40] (* _Vincenzo Librandi_, Feb 14 2012 *)

%o (MAGMA) I:=[3, 3, 7, 10]; [n le 4 select I[n] else 3*Self(n-1)-2*Self(n-2)-Self(n-3)+Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Feb 14 2012

%K nonn,easy

%O 0,1