OFFSET
0,2
COMMENTS
Sum of all second elements at level n of the TRIP-Stern sequence corresponding to the permutation triple (e,e,e)
Number of permutations of length n>0 avoiding the partially ordered pattern (POP) {1>4, 3>2} of length 4. That is, number of length n permutations having no subsequences of length 4 in which the first element is larger than the last element, and the third element is larger than the second one. - Sergey Kitaev, Dec 08 2020
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Ilya Amburg, Krishna Dasaratha, Laure Flapan, Thomas Garrity, Chansoo Lee, Cornelia Mihaila, Nicholas Neumann-Chun, Sarah Peluse, Matthew Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences, arXiv:1509.05239 [math.CO], 2015, Section 7.2.1.
Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019.
Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.
Index entries for linear recurrences with constant coefficients, signature (4,-5,4).
MATHEMATICA
CoefficientList[Series[(1-2x+3x^2)/(1-4x+5x^2-4x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -5, 4}, {1, 2, 6}, 40] (* Harvey P. Dale, Dec 27 2016 *)
PROG
(PARI) x='x+O('x^99); Vec((1-2*x+3*x^2)/(1-4*x+5*x^2-4*x^3)) \\ Altug Alkan, Apr 16 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Apr 16 2016
STATUS
approved