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A225015 Number of sawtooth patterns of length 1 in all Dyck paths of semilength n. 2
0, 1, 1, 5, 18, 66, 245, 918, 3465, 13156, 50193, 192270, 739024, 2848860, 11009778, 42642460, 165480975, 643281480, 2504501625, 9764299710, 38115568260, 148955040300, 582714871830, 2281745337300, 8942420595810, 35074414899576 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A sawtooth pattern of length 1 is UD not followed by UD.

First differences of A024482.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(0)=0, a(1)=1, a(n>1) = A024482(n) - A024482(n-1).

MAPLE

a:= proc(n) option remember; `if`(n<4, [0, 1, 1, 5][n+1],

       (n-1)*(3*n-4)*(4*n-10)*a(n-1)/(n*(n-2)*(3*n-7)))

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Apr 24 2013

CROSSREFS

Cf. A024482, A097613.

Sequence in context: A184309 A051944 A153373 * A166677 A318062 A158879

Adjacent sequences:  A225012 A225013 A225014 * A225016 A225017 A225018

KEYWORD

nonn

AUTHOR

David Scambler, Apr 23 2013

STATUS

approved

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Last modified January 21 19:42 EST 2019. Contains 319350 sequences. (Running on oeis4.)