A017818 Expansion of 1/(1-x^3-x^4-x^5).

1, 0, 0, 1, 1, 1, 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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Compositions of n into parts 3, 4, and 5. - David Neil McGrath, Jul 28 2014

The number of ways a T2 triangle can cover a row length of T1(n) triangles. - Craig Knecht, Mar 06 2025

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Tomislav Došlić, Mate Puljiz, Stjepan Šebek, and Josip Žubrinić, Predators and altruists arriving on jammed Riviera, arXiv:2401.01225 [math.CO], 2024. See p. 14.
• Craig Knecht, The number of ways a T2 triangle can cover a row of T1 triangles.
• Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,1).

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^3-x^4-x^5))); // Vincenzo Librandi, Jun 27 2013

Magma

I:=[1,0,0,1,1]; [n le 5 select I[n] else Self(n-3)+Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Jun 27 2013

Mathematica

CoefficientList[Series[1 / (1 - x^3 - x^4 - x^5), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 27 2013 *)
LinearRecurrence[{0,0,1,1,1},{1,0,0,1,1},50] (* Harvey P. Dale, Oct 03 2020 *)

Formula

a(n) = (1/10)*(2*A001608(n) + 2*A000931(n+2) + (-1)^floor(n/2) - 3(-1)^floor((n-1)/2)). - Ralf Stephan, Jun 09 2005

a(n) = a(n-5) + a(n-4) + a(n-3). - Jon E. Schoenfield, Aug 07 2006

a(2n+3) = A060945(n). - Yasuyuki Kachi, Jul 06 2024