OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-3,-1).
FORMULA
a(n) = Sum_{i=0..n} L(3i+2), L(i) = A000032(i).
a(n) = (L(3*n+4)-1)/2.
From Colin Barker, Apr 02 2019: (Start)
G.f.: (3 - x) / ((1 - x)*(1 - 4*x - x^2)).
a(n) = (-2 + (7-3*sqrt(5))*(2-sqrt(5))^n + (2+sqrt(5))^n*(7+3*sqrt(5))) / 4.
a(n) = 5*a(n-1) - 3*a(n-2) - a(n-3) for n > 2.
(End)
EXAMPLE
L(2) + L(5) = 14;
L(2) + L(5) + L(8) = 61;
L(2) + L(5) + L(8) + L(11) = 260.
MATHEMATICA
Table[(LucasL[3*n + 4] - 1)/2, {n, 0, 20}]
LinearRecurrence[{5, -3, -1}, {3, 14, 61}, 30] (* Harvey P. Dale, Aug 10 2022 *)
PROG
(PARI) L(n) = fibonacci(n+1)+fibonacci(n-1);
a(n) = (L(3*n+4)-1)/2; \\ Michel Marcus, Apr 01 2019
(PARI) Vec((3 - x) / ((1 - x)*(1 - 4*x - x^2)) + O(x^25)) \\ Colin Barker, Apr 02 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Rigoberto Florez, Apr 01 2019
STATUS
approved