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A214931 Number of self-avoiding walks of any length from NW to SW corners of a grid or lattice with 4 rows and n columns.

%I A214931 #35 Apr 09 2016 03:08:46
%S A214931 1,8,38,178,844,4012,19072,90658,430938,2048450,9737260,46285868,
%T A214931 220018976,1045856010,4971456754,23631725866,112332963420,
%U A214931 533972624844,2538228811648,12065422836242,57352760145834,272625264866098,1295919060481740,6160126839867820
%N A214931 Number of self-avoiding walks of any length from NW to SW corners of a grid or lattice with 4 rows and n columns.
%H A214931 Andrew Howroyd, <a href="/A214931/b214931.txt">Table of n, a(n) for n = 1..100</a>
%F A214931 Empirical recurrence: a(1,...,5) = (1, 8, 38, 178, 844), a(n) = 7*a(n-1) - 12*a(n-2) + 7*a(n-3) - 3*a(n-4) - 2*a(n-5). - _Giovanni Resta_, Mar 13 2013
%F A214931 Empirical g.f.: x*(1+x-6*x^2+x^3+x^4)/(1-7*x+12*x^2-7*x^3+3*x^4+2*x^5). - _Bruno Berselli_, Mar 13 2013
%e A214931 For n=2, and moves U(p), D(own), R(ight), L(eft), the a(2)=8 walks are {DDD, DRDDL, DRDLD, DDRDL, RDDDL, RDDLD, RDLDD, RDLDRDL} with only the last touching all 8 squares of the grid.
%e A214931 Illustration of the 8 walks of a(2):
%e A214931     .__      __      __        .       .        .       .     __
%e A214931      __|    .  |    .  |    |__     |__      |  .    |  .     __|
%e A214931     |  .     __|    .  |     __|     . |     |__     |  .    |__
%e A214931     |  .    |  .     __|    |  .     __|      __|    |  .     __|
%Y A214931 Row 4 of A271465.
%Y A214931 Cf. A181688 (maximal walks with same conditions).
%Y A214931 Cf. A005409 (grids with 3 rows), A006189 (grids with 3 columns).
%Y A214931 Cf. A216211 (grids with 4 columns).
%K A214931 nonn,walk
%O A214931 1,2
%A A214931 _Toby Gottfried_, Mar 09 2013
%E A214931 Missing a(7) and a(13)-a(14) from _Giovanni Resta_, Mar 13 2013
%E A214931 a(15)-a(24) from _Andrew Howroyd_, Apr 08 2016