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A338429 Maximum number of copies of a 1234 permutation pattern in an alternating (or zig-zag) permutation of length n + 5. 2
4, 8, 28, 48, 104, 160, 280, 400, 620, 840, 1204, 1568, 2128, 2688, 3504, 4320, 5460, 6600, 8140, 9680, 11704, 13728, 16328, 18928, 22204, 25480, 29540, 33600, 38560, 43520, 49504, 55488, 62628, 69768, 78204, 86640, 96520, 106400, 117880, 129360 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The maximum number of copies of 123 in an alternating permutation is motivated in the Notices reference, and the argument here is analogous.
LINKS
Lara Pudwell, From permutation patterns to the periodic table, Notices of the American Mathematical Society. 67.7 (2020), 994-1001.
FORMULA
a(2n) = A072819(n+1) = (2*n*(n + 2)*(n + 1)^2)/3.
a(2n-1) = 4*A006325(n+1) = (2*n*(n + 1)*(n^2 + n + 1))/3.
G.f.: 4*x*(1 + x^2)/((1 - x)^5*(1 + x)^3). - Stefano Spezia, Dec 12 2021
EXAMPLE
a(1) = 4. The alternating permutation of length 1+5=6 with the maximum number of copies of 1234 is 132546. The four copies are 1246, 1256, 1346, and 1356.
a(2) = 8. The alternating permutation of length 2+5=7 with the maximum number of copies of 1234 is 1325476. The eight copies are 1246, 1256, 1247, 1257, 1346, 1356, 1347, and 1357.
CROSSREFS
Sequence in context: A110132 A099513 A104042 * A117864 A020138 A306448
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Dec 01 2020
STATUS
approved

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)