Odd and even repetition sequences of independent domination number

Let {P-n}(n=1)(infinity) be a sequence of paths. The odd repetition sequence denoted by {rho(0)(k): k is an element of N} is a sequence of natural numbers in which odd numbers are repeated once and defined by {rho(0)(k)}={1,1,2,3,3,4,5,5, ...}={i(P-n)} where n = 2k - 1. The even repetition sequence denoted by {rho(e)(k): k is an element of N} is a sequence of natural numbers, in which even numbers are repeated once and defined by {rho(e)(k)}={1,2,2,3,4,4,5,6,6, ...}={i(P-n)}, where n = 2k. In this paper, the explicit formula that shows the values of the element of two sequences {rho(0)(k)} and {rho(0)(k)} that depends on the subscript.. were constructed. Also, the formula that relates the partial sum of the elements of the said sequences, which depends on the subscript.. and order of the sequence of paths, were established. Further, the independent domination number of the triangular grid graph T-m = (V (T-m), E(T-m)) will be determined using the said sequences and the two sequences will be evaluated in relation to the Fibonacci sequence {F-n} along with the order of the path.