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A033814 Convolution of positive integers n with Lucas numbers L(k)(A000032) for k >= 4.

%I A033814 #18 Jul 31 2024 07:33:44
%S A033814 7,25,61,126,238,426,737,1247,2079,3432,5628,9188,14955,24293,39409,
%T A033814 63874,103466,167534,271205,438955,710387,1149580,1860216,3010056,
%U A033814 4870543,7880881,12751717,20632902,33384934,54018162,87403433,141421943,228825735,370248048
%N A033814 Convolution of positive integers n with Lucas numbers L(k)(A000032) for k >= 4.
%H A033814 G. C. Greubel, <a href="/A033814/b033814.txt">Table of n, a(n) for n = 1..1000</a>
%H A033814 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-1,1).
%F A033814 a(n) = L(7)*(F(n+1)-1) + L(6)*F(n) - L(5)*n, F(n): Fibonacci (A000045) and L(n): Lucas (A000032).
%F A033814 G.f.: x*(7+4*x)/((1-x-x^2)*(1-x)^2).
%F A033814 a(n) = A000032(n+7) - 11*n - 29. - _G. C. Greubel_, Jun 01 2019
%t A033814 Table[LucasL[n+7] -11*n-29, {n,1,40}] (* _G. C. Greubel_, Jun 01 2019 *)
%o A033814 (PARI) vector(40, n, fibonacci(n+8) + fibonacci(n+6) -11*n-29) \\ _G. C. Greubel_, Jun 01 2019
%o A033814 (Magma) [Lucas(n+7) - 11*n - 29 : n in [1..40]]; // _G. C. Greubel_, Jun 01 2019
%o A033814 (Sage) [lucas_number2(n+7,1,-1) -11*n-29 for n in (1..40)] # _G. C. Greubel_, Jun 01 2019
%o A033814 (GAP) List([1..40], n-> Lucas(1, -1, n+7)[2] -11*n-29 ) # _G. C. Greubel_, Jun 01 2019
%o A033814 (Python)
%o A033814 from sympy import lucas
%o A033814 def a(n): return lucas(n+7) - 11*n - 29
%o A033814 print([a(n) for n in range(1, 35)]) # _Michael S. Branicky_, Jul 25 2021
%Y A033814 Cf. A000032, A000045, A023548, A023537.
%K A033814 easy,nonn
%O A033814 1,1
%A A033814 _Wolfdieter Lang_