A339356 Maximum number of copies of a 123456 permutation pattern in an alternating (or zig-zag) permutation of length n + 9.

16, 32, 144, 256, 688, 1120, 2352, 3584, 6496, 9408, 15456, 21504, 32928, 44352, 64416, 84480, 117744, 151008, 203632, 256256, 336336, 416416, 534352, 652288, 821184, 990080, 1226176, 1462272, 1785408, 2108544, 2542656, 2976768, 3550416, 4124064, 4870992, 5617920, 6577648

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..37.

Lara Pudwell, From permutation patterns to the periodic table, Notices of the American Mathematical Society. 67.7 (2020), 994-1001.

Formula

a(2n) = 32*A040977(n-1) = 64*C(n+5,6) - 32*C(n+4,5).

a(2n-1) = 16*A259181(n) = (2*n*(n + 1)*(n + 2)*(n + 3)*(2*n^2 + 6*n + 7))/45.

Example

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).

Crossrefs

Cf. A168380.

Sequence in context: A088112 A272697 A232510 * A282832 A331420 A206344

Adjacent sequences: A339353 A339354 A339355 * A339357 A339358 A339359

Keyword

nonn

Author

Lara Pudwell, Dec 01 2020

Status

approved