I. INTRODUCTIONAtanassov [9] introd

I. INTRODUCTION
Atanassov [9] introduced the interlinked second order
recurrence relation by constructing two sequences 0 { }i
∞
=
and 0 { }i
∞
= naming them as 2 – F sequences.
According to the scheme, αn + 2 = βn + 1 + βn, n ≥ 0
βn + 2 = αn + 1 + αn, n ≥ 0
Taking, α0 = a, β0 = b, α1 = c, β1 = d, where a, b, c, d
are integers, he extended his research in the same direction
which can be seen in [10], [11] and [12 ]. Hirschhorn in [14]
and [15] present explicit solutions to the longstanding
problems on the second and third order recurrence relations
posed by Atanassov [9]. Recently Singh, Sikhwal and Jain
deduced coupled recurrence relations of order five [4]. Carlitz,
et. el, [13] had also given a representation for a special
sequence.

ผลลัพธ์ (อังกฤษ) 2:

I. INTRODUCTION
Atanassov [9] introduced the Second Order interlinked
by constructing recurrence relation {0} Two sequences I
∞
=
{0} and I
∞
= Naming them As 2 - F sequences.
According to the Scheme, Αn + 2 =. Βn + 1 + Βn, n ≥ 0
Βn + 2 = Αn + 1 + Αn, n ≥ 0
Taking, Α0 = a, Β0 = B, Α1 = C, Β1 = D, where a, B, C, D
are integers. , his Research in the Extended He Same direction
which Can be seen in [10], [11] and [12]. Hirschhorn in [14]
and [15] present Explicit Solutions to the longstanding
problems on the Second and third recurrence Relations Order
posed by Atanassov [9]. Singh recently, Sikhwal and Jain
deduced coupled recurrence Relations Order of Five [4]. Carlitz,
et. el, [13] had also given a representation for a Special
Sequence.

ผลลัพธ์ (อังกฤษ) 3:

I. INTRODUCTION
Atanassov [] introduced 9 the interlinked second order
recurrence relation by constructing two sequences 0 {! I}
 ∞

{}
and 0 I  ∞
= naming them as 2 - F sequences.
According to, the scheme α N 2 = β n 1, β n n > = 0
β N 2 = α n. 1, α n n > = 0
Taking α 0 =,, a β 0 = B α 1 =,, C β 1 = D where a B C,,,,, d
are integers he extended his research in the same. Direction
.Which can be seen 10 in [], [] []. 11 and 12 Hirschhorn in [14]
and [] present 15 explicit solutions to the longstanding
problems. On the second and third order recurrence relations
posed by Atanassov []. Recently, 9 Singh Sikhwal and Jain
deduced coupled. Recurrence relations of order five []. Carlitz 4, et
. El, [] had 13 also given a representation for a special
sequence.