In this paper $q^{th}$ order linear recurrence relation is defined. This new sequence is an extension of Fibonacci sequence in such a way that the coefficients of the terms on the right hand side of its recurrence relation, are terms of the binomial expansion of $(a + b) ^{q−1}$ . Some properties of this extension like d’Ocagne ,Catalan, Cassini identities are discussed by representing the recurrence relation in Matrix form.

Key words:  $B$- Fibonacci sequence, $B$- Tribonacci sequence and $B$-$q$ bonacci sequence.

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