A116761 Number of permutations of length n which avoid the patterns 2143, 3124, 3421.

1, 2, 6, 21, 71, 220, 630, 1697, 4365, 10842, 26216, 62071, 144519, 331928, 753834, 1695933, 3784913, 8388838, 18481404, 40501523, 88342827, 191889732, 415236446, 895484281, 1925185941, 4127195570, 8824816080, 18824036847, 40063992335, 85094040112

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 33.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (9,-33,63,-66,36,-8)

Formula

G.f.: x*(1 - 7*x + 21*x^2 - 30*x^3 + 20*x^4 - 8*x^5 + 2*x^6) / ((1 - x)^3*(1 - 2*x)^3).

From Colin Barker, Oct 30 2017: (Start)

a(n) = (1/16)*(80 - 41*2^(1+n) + (56+15*2^n)*n + (8+2^n)*n^2) for n>1.

a(n) = 9*a(n-1) - 33*a(n-2) + 63*a(n-3) - 66*a(n-4) + 36*a(n-5) - 8*a(n-6) for n>7.

(End)

Prog

(PARI) Vec(x*(1 - 7*x + 21*x^2 - 30*x^3 + 20*x^4 - 8*x^5 + 2*x^6) / ((1 - x)^3*(1 - 2*x)^3) + O(x^40)) \\ Colin Barker, Oct 30 2017

Crossrefs

Sequence in context: A294701 A116749 A116792 * A116807 A294702 A116785

Adjacent sequences: A116758 A116759 A116760 * A116762 A116763 A116764

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved