A228361 The number of all possible covers of L-length line segment by 2-length line segments with allowed gaps < 2.

0, 0, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, 97229, 128801, 170625, 226030, 299426, 396655, 525456

Offset: 0

Author

Philipp O. Tsvetkov, Aug 21 2013

Keywords

• nonn
• easy

Links

• Yuksel Soykan, Vedat Irge, and Erkan Tasdemir, A Comprehensive Study of K-Circulant Matrices Derived from Generalized Padovan Numbers, Asian Journal of Probability and Statistics 26 (12):152-70, (2024). See p. 154.
• Index entries for linear recurrences with constant coefficients, signature (0,1,1).

Crossrefs

Second row of A228360.

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.

Programs

Mathematica

CoefficientList[Series[(1 - x^2 - x^3)^-1 (1 + x)^2 x^2 , {x, 0, 100}], x]

Formula

For n>1, a(n) = A134816(n).

G.f.: x^2*(1+x)^2/(1-x^2-x^3).

a(n) = a(n-2) +a(n-3) for n >= 5.

a(n) = A000931(n+5), n>1. - R. J. Mathar, Sep 02 2013