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

1,1

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.

Formula

Reference gives generating function and asymptotics.

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]]

Crossrefs

Cf. A052548, A348925.

Sequence in context: A153369 A107981 A065758 * A254028 A085274 A175648

Adjacent sequences: A348835 A348836 A348837 * A348839 A348840 A348841

Keyword

nonn

Author

Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Nov 02 2021

Status

approved