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A033814 Convolution of natural numbers n >= 1 with Lucas numbers L(k)(A000032) for k >= 4. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

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) = Lucas(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

CROSSREFS

Cf. A000032, A000045, A023548, A023537.

Sequence in context: A213392 A061600 A098538 * A321165 A118395 A118396

Adjacent sequences:  A033811 A033812 A033813 * A033815 A033816 A033817

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified January 17 23:37 EST 2020. Contains 330995 sequences. (Running on oeis4.)