A131887 Number of Khalimsky-continuous functions with a three-point codomain.

3, 5, 11, 19, 41, 71, 153, 265, 571, 989, 2131, 3691, 7953, 13775, 29681, 51409, 110771, 191861, 413403, 716035, 1542841, 2672279, 5757961, 9973081, 21489003, 37220045, 80198051, 138907099, 299303201, 518408351, 1117014753, 1934726305, 4168755811, 7220496869, 15558008491, 26947261171

Offset

1,1

Links

Neo Scott, Table of n, a(n) for n = 1..1500

Shiva Samieinia, Digital straight line segments and curves. Licentiate Thesis. Stockholm University, Department of Mathematics, Report 2007:6.

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-1).

Formula

a(2k) = a(2k-1) + a(2k-2) + a(2k-3) and a(2k-1) = a(2k-2) + 2a(2k-3).

The asymptotic behavior is a(2k) = t(2k) sqrt(3)(2 + sqrt(3))^k, a(2k-1) = t(2k-1)(2 + sqrt(3))^k where t(n) tends to 1/2 + sqrt(3)/6.

G.f.: -x*(-3-5*x+x^2+x^3) / ( 1-4*x^2+x^4 ). - R. J. Mathar, Nov 08 2013

Mathematica

LinearRecurrence[{0, 4, 0, -1}, {3, 5, 11, 19}, 40] (* Harvey P. Dale, Jan 01 2017 *)

Crossrefs

Cf. A001045, A000213, A131935, A001834 (bisection), A001835 (bisection)

Sequence in context: A285230 A089098 A129384 * A045691 A045961 A293820

Adjacent sequences: A131884 A131885 A131886 * A131888 A131889 A131890

Keyword

nonn,easy

Author

Shiva Samieinia (shiva(AT)math.su.se), Oct 05 2007, Oct 09 2007

Status

approved