A224289 Number of permutations of length n containing exactly 1 occurrence of 123 and 2 occurrences of 132.

0, 0, 0, 2, 8, 26, 79, 232, 664, 1856, 5072, 13568, 35584, 91648, 232192, 579584, 1427456, 3473408, 8359936, 19922944, 47054848, 110231552, 256311296, 591921152, 1358430208, 3099590656, 7034896384, 15888023552, 35718692864, 79960211456, 178291474432, 396076515328, 876844417024

Offset: 1

Author

Brian Nakamura, Apr 03 2013

Keywords

• nonn
• easy

Links

• B. Nakamura, Approaches for enumerating permutations with a prescribed number of occurrences of patterns, arXiv 1301.5080, 2013.
• Index entries for linear recurrences with constant coefficients, signature (8, -24, 32, -16).

Crossrefs

Cf. A000079, A001787, A001815, A046718, A001793.

Programs

Maple

# Programs can be obtained from author's personal website.

Mathematica

LinearRecurrence[{8,-24,32,-16},{0,0,0,2,8,26,79},40] (* Harvey P. Dale, Jun 23 2017 *)

Formula

a(n) = 2^(-8+n)*(-136+70*n-11*n^2+n^3) for n>3. G.f.: -x^4*(x^3-10*x^2+8*x-2) / (2*x-1)^4. - Colin Barker, Apr 14 2013