In this study, we construct the difference sequence spaces lp (P?2q) =
(lp)P?2q, 1 ? p ? ?, where P = (?rs) is an infinite matrix of Padovan
numbers %s defined by ?rs = {?s/?r+5-2 0 ? s ? r, 0 s > r. and ?2q
is a q-difference operator of second order. We obtain some inclusion
relations, topological properties, Schauder basis and ?-, ?- and ?-duals of
the newly defined space. We characterize certain matrix classes from the
space lp (P?2q) to any one of the space l1, c0, c or l?. We examine some
geometric properties and give certain estimation for von-Neumann Jordan
constant and James constant of the space lp(P). Finally, we estimate upper
bound for Hausdorff matrix as a mapping from lp to lp(P).