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

0,8

Comments

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

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.

Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,1).

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

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 *)

Prog

(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^3-x^4-x^5))); /* or */ 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

Crossrefs

Sequence in context: A116494 A036031 A218947 * A228362 A155118 A091275

Adjacent sequences: A017815 A017816 A017817 * A017819 A017820 A017821

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved