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A212342 Sequence of coefficients of x^0 in marked mesh pattern generating function Q_{n,132}^(0,3,0,0)(x). 3
1, 1, 2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90, 104, 119, 135, 152, 170, 189, 209, 230, 252, 275, 299, 324, 350, 377, 405, 434, 464, 495, 527, 560, 594, 629 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
S. Kitaev, J. Remmel and M. Tiefenbruck, Marked mesh patterns in 132-avoiding permutations I, arXiv preprint arXiv:1201.6243 [math.CO], 2012.
Kyu-Hwan Lee, Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016.
FORMULA
Conjecture: for n>=2, a(n)=(n^2+n-2)/2. - Robert Price, Jun 02 2012
Conjecture: for n>=5, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). G.f.: (1-2*x+2*x^2+x^3-x^4)/(1-x)^3. - Colin Barker, Jul 06 2012
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]); q=Simplify[Series[QQ3[t, x], {t, 0, 35}]]; CoefficientList[q /. x -> 0, t] (* Robert Price, Jun 04 2012 *)
CROSSREFS
A201163 is similar. - Robert Price, Jun 02 2012
Sequence in context: A079509 A132336 A272370 * A080956 A132337 A000096
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, May 09 2012
EXTENSIONS
a(10)-a(35) from Robert Price, Jun 02 2012
Added a(0) to correspond to given offset and to be consistent with A212346, Robert Price, Jun 02 2012
STATUS
approved

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Last modified February 24 14:59 EST 2024. Contains 370305 sequences. (Running on oeis4.)