|
%I #19 Oct 18 2022 14:57:37
%S 1,2,4,8,11,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,
%T 92,96,100,104,108,112,116,120,124,128,132,136,140,144,148,152,156,
%U 160,164,168,172,176,180,184,188,192,196,200,204,208,212,216,220,224
%N Coordination sequence for the Manhattan lattice.
%C In the Manhattan lattice, N-S streets run alternately N and S, and E-W streets run alternately E and W. - _N. J. A. Sloane_, Jul 29 2020
%H Sean A. Irvine, <a href="/A336627/a336627.png">Illustration of a(0) to a(7)</a>
%H N. J. A. Sloane, <a href="/A336627/a336627_1.png">Crude drawing of initial layers showing paths of length 6 from origin</a> (looking North-West). The presence of three points at distance 4 from the origin on the line of symmetry explains why a(4) is odd!
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F G.f.: (1+x^2) * (1+2*x^3-x^4) / (1-x)^2.
%F a(n) = 4*(n-1), n >= 5.
%t CoefficientList[Series[(1+x^2)(1+2x^3-x^4)/(1-x)^2,{x,0,80}],x] (* or *) LinearRecurrence[{2,-1},{1,2,4,8,11,16,20},80] (* _Harvey P. Dale_, Dec 28 2021 *)
%o (PARI) a(n)=if(n>4, 4*n-4, min(2^n, 11)) \\ _Charles R Greathouse IV_, Oct 18 2022
%Y Cf. A008574 (square lattice), A117633 (self-avoiding walks).
%K nonn,nice,easy
%O 0,2
%A _Sean A. Irvine_, Jul 28 2020
|
