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A033814
Convolution of positive integers n with Lucas numbers L(k)(A000032) for k >= 4.
3
7, 25, 61, 126, 238, 426, 737, 1247, 2079, 3432, 5628, 9188, 14955, 24293, 39409, 63874, 103466, 167534, 271205, 438955, 710387, 1149580, 1860216, 3010056, 4870543, 7880881, 12751717, 20632902, 33384934, 54018162, 87403433, 141421943, 228825735, 370248048
OFFSET
1,1
FORMULA
a(n) = L(7)*(F(n+1)-1) + L(6)*F(n) - L(5)*n, F(n): Fibonacci (A000045) and L(n): Lucas (A000032).
G.f.: x*(7+4*x)/((1-x-x^2)*(1-x)^2).
a(n) = A000032(n+7) - 11*n - 29. - G. C. Greubel, Jun 01 2019
MATHEMATICA
Table[LucasL[n+7] -11*n-29, {n, 1, 40}] (* G. C. Greubel, Jun 01 2019 *)
PROG
(PARI) vector(40, n, fibonacci(n+8) + fibonacci(n+6) -11*n-29) \\ G. C. Greubel, Jun 01 2019
(Magma) [Lucas(n+7) - 11*n - 29 : n in [1..40]]; // G. C. Greubel, Jun 01 2019
(Sage) [lucas_number2(n+7, 1, -1) -11*n-29 for n in (1..40)] # G. C. Greubel, Jun 01 2019
(GAP) List([1..40], n-> Lucas(1, -1, n+7)[2] -11*n-29 ) # G. C. Greubel, Jun 01 2019
(Python)
from sympy import lucas
def a(n): return lucas(n+7) - 11*n - 29
print([a(n) for n in range(1, 35)]) # Michael S. Branicky, Jul 25 2021
CROSSREFS
KEYWORD
easy,nonn
STATUS
approved