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 A339358 Maximum number of copies of a 1234567 permutation pattern in an alternating (or zig-zag) permutation of length n + 11. 1
 32, 64, 320, 576, 1696, 2816, 6400, 9984, 19392, 28800, 50304, 71808, 116160, 160512, 244992, 329472, 480480, 631488, 887744, 1144000, 1560416, 1976832, 2629120, 3281408, 4271488, 5261568, 6723840, 8186112, 10294656, 12403200, 15379968, 18356736, 22480800, 26604864 (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 Table of n, a(n) for n=1..34. Lara Pudwell, From permutation patterns to the periodic table, Notices of the American Mathematical Society. 67.7 (2020), 994-1001. FORMULA a(2n) = 64*A050486(n-1) = 128*C(n+6,7) - 64*C(n+5,6). a(2n-1) = 128*C(n+4,7) + 128*C(n+4,6) + 32*C(n+4,5). D-finite with recurrence (-n+1)*a(n) +2*a(n-1) +16*a(n-2) +2*a(n-3) +(n+7)*a(n-4)=0. - R. J. Mathar, Jan 11 2024 EXAMPLE a(1) = 32. The alternating permutation of length 1+11=12 with the maximum number of copies of 1234567 is 132547698(11)(10)(12). The 32 copies are 12468(10)(12), 12469(10)(12), 12478(10)(12), 12479(10)(12), 12568(10)(12), 12569(10)(12), 12578(10)(12), 12579(10)(12), 13468(10)(12), 13469(10)(12), 13478(10)(12), 13479(10)(12), 13568(10)(12), 13569(10)(12), 13578(10)(12), 13579(10)(12), 12468(11)(12), 12469(11)(12), 12478(11)(12), 12479(11)(12), 12568(11)(12), 12569(11)(12), 12578(11)(12), 12579(11)(12), 13468(11)(12), 13469(11)(12), 13478(11)(12), 13479(11)(12), 13568(11)(12), 13569(11)(12), 13578(11)(12), and 13579(11)(12). MAPLE A339358 := proc(n) nhalf := ceil(n/2) ; if type(n, 'even') then 128*binomial(nhalf+6, 7)-64*binomial(nhalf+5, 6) ; else 128*binomial(nhalf+4, 7)+128*binomial(nhalf+4, 6)+32*binomial(nhalf+4, 5) ; end if; end proc: seq(A339358(n), n=1..40) ; # R. J. Mathar, Jan 11 2024 CROSSREFS Cf. A168380. Sequence in context: A256819 A358250 A235057 * A249116 A110562 A275187 Adjacent sequences: A339355 A339356 A339357 * A339359 A339360 A339361 KEYWORD nonn AUTHOR Lara Pudwell, Dec 01 2020 STATUS approved

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Last modified August 13 09:05 EDT 2024. Contains 375118 sequences. (Running on oeis4.)