OFFSET
1,2
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Darla Kremer and Wai Chee Shiu, Finite transition matrices for permutations avoiding pairs of length four patterns, Discrete Math. 268 (2003), 171-183. MR1983276 (2004b:05006). See Table 1.
V. Vatter, Finding regular insertion encodings for permutation classes, Journal of Symbolic Computation, Volume 47, Issue 3, March 2012, Pages 259-265.
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
FORMULA
G.f.: (1-11*x-413*x^7+217*x^8+554*x^6-2*x^11+357*x^4 -83*x^9-519*x^5 +20*x^10 +56*x^2-172*x^3) / (1-x)^12.
a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>12. - Colin Barker, Oct 31 2017
EXAMPLE
There are 22 permutations of length 4 which avoid these two patterns, so a(4)=22.
MATHEMATICA
CoefficientList[Series[(1-11*x-413*x^7+217*x^8+554*x^6-2*x^11+357*x^4 -83*x^9-519*x^5 +20*x^10 +56*x^2-172*x^3)/(1-x)^12, {x, 0, 50}], x] (* G. C. Greubel, Oct 21 2018 *)
LinearRecurrence[{12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1}, {1, 2, 6, 22, 86, 332, 1217, 4140, 12934, 37088, 98115, 241269}, 40] (* Harvey P. Dale, Jan 03 2019 *)
PROG
(PARI) Vec(x*(1 - 10*x + 48*x^2 - 138*x^3 + 273*x^4 - 370*x^5 + 379*x^6 - 278*x^7 + 137*x^8 - 46*x^9 + 10*x^10 - x^11) / (1 - x)^12 + O(x^40)) \\ Colin Barker, Oct 31 2017
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-11*x-413*x^7+217*x^8+554*x^6-2*x^11+357*x^4 -83*x^9-519*x^5 +20*x^10 +56*x^2-172*x^3)/(1-x)^12)); // G. C. Greubel, Oct 21 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincent Vatter, Sep 21 2009
STATUS
approved