Two sequences with sod: more terms?

[hv at crypt.org]

sense (though far more mildly so than its origins might suggest). I would
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Date: Sun, 10 Feb 2008 09:58:33 -0800 (PST)
From: Leroy Quet <q1qq2qqq3qqqq at yahoo.com>
Subject: Up/Down-Symmetric Permutations
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This post deals with two kinds of permutations.


Let us say we have the permutation
(p(1),p(2),...,p(n)) of (1,2,...,n)
where, for each k (2<=k<=n), the sign of
(p(k) - p(k-1)) equals the sign of 
(p(n+2-k) - p(n+1-k)).

For example: Such a permutation (for n = 7) would
be:
3,6,7,5,1,2,4

The signs of the differences between adjacent
terms forms the sequence: ++--++, which has
reflective symmetry.

Is the sequence, where a(n) equals the number of
such permutations for n, in the EIS already?

--

Let us say we have the permutation
(p(1),p(2),...,p(n)) of (1,2,...,n)
where, for each k (2<=k<=n), the sign of
(p(k) - p(k-1)) equals the sign of 
(p(n+1-k) - p(n+2-k)).

For example: Such a permutation (for n = 7) would
be:
3,4,5,2,7,6,1

The signs of the differences between adjacent
terms forms the sequence: ++-+--, which is the
negative of its reversal.

Is the sequence, where a(n) equals the number of
such permutations for n, in the EIS already?


Note: a(2n) = 0 for all n, in regards to the
latter sequence, since there are an odd number of
signs, and the middle sign can't equal its
negative.


If one or both of these sequences isn't in the
EIS already, could someone please calculate and
submit it/them?
Thanks.

Thank you,
Leroy Quet




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