Leonardo numbers

The Leonardo numbers are a sequence of numbers defined by:

L(0) = 1 || 0
L(1) = 1 || 0
L(x) = L(x - 1) + L(x - 2) + 1

Generalizing the above a bit more:

L(x) = L(x - 1) + L(x - 2) + a

Assume a to be the add number.

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Task

Return the first n Leonardo numbers as an array (vector<int> in C++)

Input

• n : The number of Leonardo numbers to be shown
• L0 : The initial value of L(0)
• L1 : The initial value of L(1)
• add : The add number

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Examples

input  : n = 5 , L0 = 1 , L1 = 1 , add = 1
output : [ 1, 1, 3, 5, 9 ]

input  : n = 5 , L0 = 0 , L1 = 0 , add = 2
output : [ 0, 0, 2, 4, 8 ]

input  : n = 10 , L0 = 0 , L1 = 1 , add = 4
output : [ 0, 1, 5, 10, 19, 33, 56, 93, 153, 250 ]

input  : n = 5 , L0 = 0 , L1 = 0 , add = 0
output : [ 0, 0, 0, 0, 0 ]

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Note

n will always be greater than or equal to 2