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A033814 Convolution of natural numbers n >= 1 with Lucas numbers L(k)(A000032) for k >= 4. 2

%I

%S 7,25,61,126,238,426,737,1247,2079,3432,5628,9188,14955,24293,39409,

%T 63874,103466,167534,271205,438955,710387,1149580,1860216,3010056,

%U 4870543,7880881,12751717,20632902,33384934,54018162

%N Convolution of natural numbers n >= 1 with Lucas numbers L(k)(A000032) for k >= 4.

%H G. C. Greubel, <a href="/A033814/b033814.txt">Table of n, a(n) for n = 1..1000</a>

%F 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 G.f.: x*(7+4*x)/((1-x-x^2)*(1-x)^2).

%F a(n) = Lucas(n+7) - 11*n - 29. - _G. C. Greubel_, Jun 01 2019

%t Table[LucasL[n+7] -11*n-29, {n,1,40}] (* _G. C. Greubel_, Jun 01 2019 *)

%o (PARI) vector(40, n, fibonacci(n+8) + fibonacci(n+6) -11*n-29) \\ _G. C. Greubel_, Jun 01 2019

%o (MAGMA) [Lucas(n+7) - 11*n - 29 : n in [1..40]]; // _G. C. Greubel_, Jun 01 2019

%o (Sage) [lucas_number2(n+7,1,-1) -11*n-29 for n in (1..40)] # _G. C. Greubel_, Jun 01 2019

%o (GAP) List([1..40], n-> Lucas(1, -1, n+7)[2] -11*n-29 ) # _G. C. Greubel_, Jun 01 2019

%Y Cf. A000032, A000045, A023548, A023537.

%K easy,nonn

%O 1,1

%A _Wolfdieter Lang_

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Last modified February 25 23:44 EST 2020. Contains 332270 sequences. (Running on oeis4.)