A007486 a(n) = a(n-1) + a(n-2) + a(n-3). (Formerly M2351)

1, 3, 4, 8, 15, 27, 50, 92, 169, 311, 572, 1052, 1935, 3559, 6546, 12040, 22145, 40731, 74916, 137792, 253439, 466147, 857378, 1576964, 2900489, 5334831, 9812284, 18047604, 33194719, 61054607, 112296930, 206546256, 379897793, 698740979, 1285185028

Offset

1,2

Comments

If A001590 is the tribonacci sequence, this might be called the Trucas sequence after the Lucas sequence A000032. - Paul Wayper (paulway(AT)mabula.net), Nov 28 2007

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence)

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

N. G. Voll, Some identities for four term recurrence relations, Fib. Quart., 51 (2013), 268-273.

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

Formula

O.g.f.: x*(1+2*x)/(1-x-x^2-x^3). a(n) = A001590(n)+3*A000073(n). - R. J. Mathar, Aug 22 2008

a(n) = 2*a(n-1) - a(n-4), n>4. - Vincenzo Librandi, Jun 08 2011

Mathematica

LinearRecurrence[{1, 1, 1}, {1, 3, 4}, 100] (* Vladimir Joseph Stephan Orlovsky, Jun 07 2011 *)
CoefficientList[Series[(1 + 2 x) / (1 - x - x^2 - x^3), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 09 2013 *)

Prog

(PARI) Vec((x+2*x^2)/(1-x-x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2011
(Magma) I:=[1, 3, 4]; [n le 3 select I[n] else Self(n-1)+Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jun 09 2013

Crossrefs

Cf. A001590, A000032, A000045.

Sequence in context: A033854 A042981 A337438 * A027977 A165438 A293781

Adjacent sequences: A007483 A007484 A007485 * A007487 A007488 A007489

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved