A023537 -id:A023537 - cp's OEIS frontend

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

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

Wolfdieter Lang

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).

Cf. A000032, A000045, A023548, A023537.

List([1..40], n-> Lucas(1, -1, n+7)[2] -11*n-29 ) # G. C. Greubel, Jun 01 2019

[Lucas(n+7) - 11*n - 29 : n in [1..40]]; // G. C. Greubel, Jun 01 2019

Table[LucasL[n+7] -11*n-29, {n,1,40}] (* G. C. Greubel, Jun 01 2019 *)

vector(40, n, fibonacci(n+8) + fibonacci(n+6) -11*n-29) \\ G. C. Greubel, Jun 01 2019

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

[lucas_number2(n+7,1,-1) -11*n-29 for n in (1..40)] # G. C. Greubel, Jun 01 2019

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

A033817 Convolution of natural numbers n >= 1 with Lucas numbers L(k) for k >= -4.

Original entry on oeis.org

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

Offset: 1

Wolfdieter Lang

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3, -2, -1, 1).

Cf. A000032, A000045, A023548, A023537, A033814.

List([1..40], n-> Lucas(1, -1, n-1)[2] +4*n+1 ) # G. C. Greubel, Jun 01 2019

[Lucas(n-1) + 4*n + 1 : n in [1..40]]; // G. C. Greubel, Jun 01 2019

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

vector(40, n, fibonacci(n) + fibonacci(n-2) +4*n+1) \\ G. C. Greubel, Jun 01 2019

[lucas_number2(n-1,1,-1) +4*n+1 for n in (1..40)] # G. C. Greubel, Jun 01 2019

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*(7-11*x)/((1-x-x^2)*(1-x)^2).
a(n) = Lucas(n-1) + 4*n + 1. - G. C. Greubel, Jun 01 2019

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

cp's OEIS Frontend

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

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