A282718 Satisfies the tribonacci recurrence: a(n) = a(n-1) + a(n-2) + a(n-3).

0, 1, 3, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012, 121415, 223317, 410744, 755476, 1389537, 2555757, 4700770, 8646064, 15902591, 29249425, 53798080, 98950096, 181997601, 334745777, 615693474

Offset: 0

Author

N. J. A. Sloane, Mar 02 2017

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Julien Leroy, Michel Rigo, and Manon Stipulanti, Counting the number of non-zero coefficients in rows of generalized Pascal triangles Discrete Mathematics 340 (2017), 862-881. See Example 43.
• Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, Integer sequences from k-iterated line digraphs, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
• Index entries for linear recurrences with constant coefficients, signature (1,1,1).

Crossrefs

Cf. A000073.

Programs

Magma

I:=[0,1,3,4,7,13]; [n le 6 select I[n] else Self(n-1)+Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Mar 28 2017

Mathematica

Join[{0, 1, 3}, LinearRecurrence[{1, 1, 1}, {4, 7, 13}, 20]] (* Vincenzo Librandi, Mar 28 2017 *)

Formula

a(n) = A000073(n+2), n >= 3. - R. J. Mathar, Mar 03 2017

G.f.: x*(1 + 2*x - x^3 - x^4)/(1 - x - x^2 - x^3). - Bruno Berselli, Mar 03 2017