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A131887 Number of Khalimsky-continuous functions with a three-point codomain. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 08:35 EST 2022. Contains 358515 sequences. (Running on oeis4.)