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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Mathematica

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

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