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A212346 Sequence of coefficients of x^0 in marked mesh pattern generating function Q_{n,132}^(0,4,0,0)(x). 2
1, 1, 2, 5, 14, 28, 48, 75, 110, 154, 208, 273, 350, 440, 544, 663, 798, 950, 1120, 1309, 1518, 1748, 2000, 2275, 2574, 2898, 3248, 3625, 4030, 4464, 4928, 5423, 5950, 6510, 7104, 7733 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Conjecture stated in Formula holds through a(35).
LINKS
S. Kitaev, J. Remmel and M. Tiefenbruck, Marked mesh patterns in 132-avoiding permutations I, arXiv preprint arXiv:1201.6243, 2012
FORMULA
Conjecture: this appears to equal (n+3)(n^2-4)/6 for n >= 3, see A129936.
Conjectures from Colin Barker, Feb 11 2015: (Start)
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>6.
G.f.: (2*x^6-5*x^5+3*x^4-x^3+4*x^2-3*x+1) / (x-1)^4.
(End)
MATHEMATICA
QQ0[t, x] = (1 - (1-4*x*t)^(1/2)) / (2*x*t); QQ1[t, x] = 1/(1 - t*QQ0[t, x]); QQ2[t, x] = (1 + t*(QQ1[t, x] - QQ0[t, x]))/(1 - t*QQ0[t, x]); QQ3[t, x] = (1 + t*(QQ2[t, x] - QQ0[t, x] + t*(QQ1[t, x] - QQ0[t, x])))/(1 - t*QQ0[t, x]); QQ4[t, x] = (1 + t*(QQ3[t, x] - QQ0[t, x] + t*(QQ2[t, x] - QQ0[t, x]) + (2*t^2*(QQ1[t, x] - QQ0[t, x]))))/(1 - t*QQ0[t, x]); q=Simplify[Series[QQ4[t, x], {t, 0, 35}]]; CoefficientList[q /. x -> 0, t] (* Robert Price, Jun 04 2012 *)
CROSSREFS
Sequence in context: A341896 A214203 A100779 * A194124 A349094 A212340
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, May 09 2012
EXTENSIONS
a(10)-a(35) from Robert Price, Jun 02 2012
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)