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%I #6 Dec 01 2020 20:47:59
%S 16,32,144,256,688,1120,2352,3584,6496,9408,15456,21504,32928,44352,
%T 64416,84480,117744,151008,203632,256256,336336,416416,534352,652288,
%U 821184,990080,1226176,1462272,1785408,2108544,2542656,2976768,3550416,4124064,4870992,5617920,6577648
%N Maximum number of copies of a 123456 permutation pattern in an alternating (or zig-zag) permutation of length n + 9.
%C The maximum number of copies of 123 in an alternating permutation is motivated in the Notices reference, and the argument here is analogous.
%H Lara Pudwell, <a href="https://www.ams.org/journals/notices/202007/rnoti-p994.pdf">From permutation patterns to the periodic table</a>, Notices of the American Mathematical Society. 67.7 (2020), 994-1001.
%F a(2n) = 32*A040977(n-1) = 64*C(n+5,6) - 32*C(n+4,5).
%F a(2n-1) = 16*A259181(n) = (2*n*(n + 1)*(n + 2)*(n + 3)*(2*n^2 + 6*n + 7))/45.
%e a(1) = 16. The alternating permutation of length 1+9=10 with the maximum number of copies of 123456 is 132547698(10). The sixteen copies are 12468(10), 12469(10), 12478(10), 12479(10), 12568(10), 12569(10), 12578(10), 12579(10), 13468(10), 13469(10), 13478(10), 13479(10), 13568(10), 13569(10), 13578(10), and 13579(10).
%Y Cf. A168380.
%K nonn
%O 1,1
%A _Lara Pudwell_, Dec 01 2020
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