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Article: Smarandache Pascal derived sequences.
- Article from:
- Smarandache Notions Journal
- Article date:
- January 1, 2001
- Author:
CopyrightCOPYRIGHT 2001 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Given a sequence say [S.sub.b]. We call it the base sequence. We define a Smarandache Pascal derived sequence [S.sub.d] as follows:
[T.sub.n+1] = [n.summation over (k=0)][sup.r][C.sub.k] x [t.sub.k+1], where [t.sub.k] is the kth term of the base sequence.
Let the terms of the the base sequence [S.sub.b] be [b.sub.1], [b.sub.2], [b.sub.3], [b.sub.4],... Then the Smarandache Pascal derived Sequence [S.sub.d] [d.sub.1], [d.sub.2], [d.sub.3], [d.sub.4],... is defined as follows: [d.sub.1] = [b.sub.1] [d.sub.2] = [b.sub.1] + [b.sub.2] [d.sub.3] = [b.sub.1] + 2[b.sub.2] + [b.sub.3] [d.sub.4] = [v.sub.1] + 3[b.sub.2] + 3[b.sub.3] + [b.sub.4]
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