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%I #9 Jul 31 2015 11:00:05
%S 4,15,37,77,146,262,454,769,1283,2119,3476,5676,9240,15011,24353,
%T 39473,63942,103538,167610,271285,439039,710475,1149672,1860312,
%U 3010156,4870647,7880989,12751829,20633018,33385054
%N Convolution of natural numbers n >= 1 with Lucas numbers L(k)(A000032) for k >= 3.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, -1, 1).
%F a(n)=L(6)*(F(n+1)-1)+L(5)*F(n)-L(4)*n, F(n): Fibonacci (A000045), G.F. x*(4+3*x)/((1-x-x^2)*(1-x)^2)
%F a(0)=4, a(1)=15, a(2)=37, a(3)=77, a(n)=3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4) [From Harvey P. Dale, May 23 2011]
%t LinearRecurrence[{3,-2,-1,1},{4,15,37,77},40] (* or *) Rest[ CoefficientList[ Series[x (4+3x)/((1-x-x^2)(1-x)^2),{x,0,40}],x]](* _Harvey P. Dale_, May 23 2011 *)
%Y Cf. A023548, A023553.
%K easy,nonn
%O 1,1
%A _Wolfdieter Lang_
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