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Article: Depascalisation of Smarandache Pascal derived sequences and backward extended Fibonacci sequence.
- 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 [S.sub.b] (called the base sequence). [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: Ref[1] [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] = [b.sub.1] + 3[b.sub.2] + 3[b.sub.3] + [b.sub.4]
[d.sub.n+1] = [n.summation over (k=0)][sup.n][C.sub.k] x [b.sub.k+1]
Now Given [S.sub.d] the task ahead is to find out the base sequence [S.sub.b]. We call the process of extracting the base sequence from the Pascal derived sequence as Depascalisation. The ...
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