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%I #27 Jan 10 2025 04:38:47
%S 0,0,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,265,351,465,
%T 616,816,1081,1432,1897,2513,3329,4410,5842,7739,10252,13581,17991,
%U 23833,31572,41824,55405,73396,97229,128801,170625,226030,299426,396655,525456
%N The number of all possible covers of L-length line segment by 2-length line segments with allowed gaps < 2.
%H Yuksel Soykan, Vedat Irge, and Erkan Tasdemir, <a href="https://doi.org/10.9734/ajpas/2024/v26i12691">A Comprehensive Study of K-Circulant Matrices Derived from Generalized Padovan Numbers</a>, Asian Journal of Probability and Statistics 26 (12):152-70, (2024). See p. 154.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1).
%F For n>1, a(n) = A134816(n).
%F G.f.: x^2*(1+x)^2/(1-x^2-x^3).
%F a(n) = a(n-2) +a(n-3) for n >= 5.
%F a(n) = A000931(n+5), n>1. - _R. J. Mathar_, Sep 02 2013
%t CoefficientList[Series[(1 - x^2 - x^3)^-1 (1 + x)^2 x^2 , {x, 0, 100}], x]
%Y Second row of A228360.
%Y The following are basically all variants of the same sequence: A000931, A078027, A096231, A124745, A133034, A134816, A164001, A182097, A228361 and probably A020720. However, each one has its own special features and deserves its own entry.
%K nonn,easy
%O 0,4
%A _Philipp O. Tsvetkov_, Aug 21 2013