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A116847
Number of permutations of length n which avoid the patterns 123, 51432.
1
1, 2, 5, 14, 41, 119, 336, 924, 2492, 6636, 17536, 46137, 121095, 317434, 831571, 2177734, 5702191, 14929519, 39087182, 102332996, 267912946, 701407172, 1836310110, 4807524929, 12586266701, 32951277474, 86267568321, 225851430414, 591286726197, 1548008751831
OFFSET
1,2
LINKS
Myrto Kallipoliti, Robin Sulzgruber, and Eleni Tzanaki, Patterns in Shi tableaux and Dyck paths, arXiv:2006.06949 [math.CO], 2020.
FORMULA
G.f.: x*(1 - 5*x + 10*x^2 - 9*x^3 + 5*x^4 - x^5) / ((1 - x)^4*(1 - 3*x + x^2)).
a(n) = A001906(n) - A004006(n-1). - R. J. Mathar, Jan 12 2013
a(n) = 1 - ((3-sqrt(5))/2)^n/sqrt(5) + ((3+sqrt(5))/2)^n/sqrt(5) - (4*n)/3 + n^2/2 - n^3/6. - Colin Barker, Oct 31 2017
PROG
(PARI) Vec(x*(1 - 5*x + 10*x^2 - 9*x^3 + 5*x^4 - x^5) / ((1 - x)^4*(1 - 3*x + x^2)) + O(x^40)) \\ Colin Barker, Oct 31 2017
CROSSREFS
Sequence in context: A116851 A038989 A116850 * A116848 A370800 A122055
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved