A348838 Number of 3-sided prudent polygons of area n.
6, 10, 20, 42, 92, 204, 454, 1010, 2242, 4962, 10946, 24066, 52736, 115186, 250800, 544432, 1178432, 2543712, 5476352, 11760642, 25196566, 53861008, 114889430, 244571174, 519630462, 1102021562, 2333088968, 4931232086, 10406327848, 21927562520, 46138651012
Offset: 1
Keywords
Links
- Nicholas R. Beaton and Anthony Guttmann, Table of n, a(n) for n = 1..3200
- Nicholas R. Beaton, Philippe Flajolet and Anthony J. Guttmann, The Enumeration of Prudent Polygons by Area and its Unusual Asymptotics, arXiv:1011.6195 [math.CO], Nov 29, 2010.
- Nicholas R. Beaton, Philippe Flajolet and Anthony J. Guttmann, The Enumeration of Prudent Polygons by Area and its Unusual Asymptotics, J. Comb. Theory Series A vol.118, 2011, pp.2261-2290.
- Nicholas R. Beaton, Philippe Flajolet, Tim Garoni and Anthony J. Guttmann, Some New Self-avoiding Walk and Polygon Models, Fundamenta Informaticae, vol. 117, 2012, pp. 19-33.
Programs
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Mathematica
nmax = 40; Rest[CoefficientList[Series[2*q*(3 - 10*q + 9*q^2 - q^3)/((1 - 2*q)^2*(1 - q)) - 2*q^3*(1 - q)^2/(1 - 2*q)^2 * Sum[(-1)^m * q^(2*m) / ((1 - 2*q)^m*(1 - q - q^(m + 1))) * Product[(1 - q - q^k + q^(k+1) - q^(k+2)) / (1 - q - q^(k+1)), {k, 1, m-1}], {m, 1, nmax}], {q, 0, nmax}], q]]
Formula
Reference gives generating function and asymptotics.