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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
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
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Dec 01 2020
STATUS
approved