

A033817


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


1



7, 10, 16, 21, 28, 36, 47, 62, 84, 117, 168, 248, 375, 578, 904, 1429, 2276, 3644, 5855, 9430, 15212, 24565, 39696, 64176, 103783, 167866, 271552, 439317, 710764, 1149972, 1860623, 3010478, 4870980, 7881333, 12752184, 20633384, 33385431, 54018674, 87403960, 141422485
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OFFSET

1,1


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = L(1)*(F(n+1)1) + L(2)*F(n)  L(3)*n, F(n): Fibonacci (A000045), L(n): Lucas (A000032) with L(n)=(1)^n*L(n)
G.f.: x*(711*x)/((1xx^2)*(1x)^2).
a(n) = Lucas(n1) + 4*n + 1.  G. C. Greubel, Jun 01 2019


MATHEMATICA

Table[LucasL[n1] +4*n+1, {n, 1, 40}] (* G. C. Greubel, Jun 01 2019 *)


PROG

(PARI) vector(40, n, fibonacci(n) + fibonacci(n2) +4*n+1) \\ G. C. Greubel, Jun 01 2019
(MAGMA) [Lucas(n1) + 4*n + 1 : n in [1..40]]; // G. C. Greubel, Jun 01 2019
(Sage) [lucas_number2(n1, 1, 1) +4*n+1 for n in (1..40)] # G. C. Greubel, Jun 01 2019
(GAP) List([1..40], n> Lucas(1, 1, n1)[2] +4*n+1 ) # G. C. Greubel, Jun 01 2019


CROSSREFS

Cf. A000032, A000045, A023548, A023537, A033814.
Sequence in context: A234093 A287567 A301451 * A286873 A218128 A175666
Adjacent sequences: A033814 A033815 A033816 * A033818 A033819 A033820


KEYWORD

easy,nonn


AUTHOR

Wolfdieter Lang


EXTENSIONS

Terms a(31) onward added by G. C. Greubel, Jun 01 2019


STATUS

approved



