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 A339355 Maximum number of copies of a 12345 permutation pattern in an alternating (or zig-zag) permutation of length n + 7. 1
 8, 16, 64, 112, 272, 432, 832, 1232, 2072, 2912, 4480, 6048, 8736, 11424, 15744, 20064, 26664, 33264, 42944, 52624, 66352, 80080, 99008, 117936, 143416, 168896, 202496, 236096, 279616, 323136, 378624, 434112, 503880, 573648, 660288, 746928, 853328, 959728, 1089088, 1218448 (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 Georg Fischer, Table of n, a(n) for n = 1..200 Lara Pudwell, From permutation patterns to the periodic table, Notices of the American Mathematical Society. 67.7 (2020), 994-1001. FORMULA a(2*n) = 16*A005585(n) = 32*binomial(n+4, 5) - 16*binomial(n+3, 4). a(2*n-1) = 8*A033455(n) = (4*n*(n^4 + 5*n^3 + 10*n^2 + 10*n + 4))/15. D-finite with recurrence: (n-1)*((n-3)^2+9*n-6)*a(n) - (2*(n-3)^2+20*n-16)*a(n-1) - (n+5)*((n-3)^2+11*n-2)*a(n-2) = 0. - Georg Fischer, Nov 25 2022 EXAMPLE a(1) = 8. The alternating permutation of length 1 + 7 = 8 with the maximum number of copies of 12345 is 13254768. The eight copies are 12468, 12478, 12568, 12578, 13468, 13478, 13568, and 13578. MAPLE a := proc(n2) local n; n:= floor(n2/2): if n2 = 2*n then 32*binomial(n+4, 5) - 16*binomial(n+3, 4) else n:=n+1; (4*n*(n^4+5*n^3+10*n^2+10*n+4))/15 fi end; seq(a(n), n=1..20); # Georg Fischer, Nov 25 2022 CROSSREFS Cf. A005585, A033455, A168380. Sequence in context: A307876 A166638 A356961 * A132794 A082982 A218899 Adjacent sequences: A339352 A339353 A339354 * A339356 A339357 A339358 KEYWORD nonn AUTHOR Lara Pudwell, Dec 01 2020 STATUS approved

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Last modified September 12 12:42 EDT 2024. Contains 375851 sequences. (Running on oeis4.)