A228362 The number of all possible covers of L-length line segment by 3-length line segments with allowed gaps < 3.

0, 0, 0, 1, 2, 3, 3, 4, 6, 8, 10, 13, 18, 24, 31, 41, 55, 73, 96, 127, 169, 224, 296, 392, 520, 689, 912, 1208, 1601, 2121, 2809, 3721, 4930, 6531, 8651, 11460, 15182, 20112, 26642, 35293, 46754, 61936, 82047, 108689, 143983, 190737

Offset

0,5

Comments

For n>2, a(n) = A017818(n+3).

Links

Table of n, a(n) for n=0..45.

Formula

G.f.: x^3*(1 + x + x^2)^2 / (1 - x^3 - x^4 - x^5).

a(0)=a(1)=a(2)=0; a(3)=1; a(4)=2; a(5)= a(6)=3; a(7)=4; a(n)= a(n-3) + a(n-4) + a(n-5).

Mathematica

CoefficientList[Series[(1 - x^3 - x^4 - x^5)^-1*(1 + x + x^2)^2*x^3 , {x, 0, 100}], x]

Crossrefs

Third row of A228360.

Sequence in context: A036031 A218947 A017818 * A155118 A091275 A046936

Adjacent sequences: A228359 A228360 A228361 * A228363 A228364 A228365

Keyword

nonn

Author

Philipp O. Tsvetkov, Aug 21 2013

Status

approved