0,1

M. Elia. "Derived Sequences, The Tribonacci Recurrence and Cubic Forms." The Fibonacci Quarterly 39.2 (2001): 107-109

G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.

Fielder, Daniel C.; Special integer sequences controlled by three parameters. Fibonacci Quart 6 1968 64-70.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.4.

T. D. Noe, Table of n, a(n) for n=0..200

G. Everest, A. J. van der Poorten, Y. Puri and T. Ward, Integer Sequences and Periodic Points, Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.3

G. Everest, Y. Puri and T. Ward, Integer sequences counting periodic points

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Eric Weisstein's World of Mathematics, Lucas n-Step Number

Eric Weisstein's World of Mathematics, Tribonacci Number

Binet's formula: a(n)=r1^n+r2^n+r3^n, where r1, r2, r3 are the roots of the characteristic polynomial 1+x+x^2-x^3.

G.f.: g(x)=(3-2*x-x^2)/(1-x-x^2-x^3) - Miklos Kristof (kristmikl(AT)freemail.hu), Jul 29 2002

A001644:=-(1+2*z+3*z**2)/(z**3+z**2+z-1); [Conjectured by S. Plouffe in his 1992 dissertation. Gives sequence except for the initial 3.]

f[x_] := f[x] = f[x - 1] + f[x - 2] + f[x - 3]; f[0] = 3; f[1] = 1; f[2] = 3

(PARI) a(n)=if(n<0, 0, polsym(1+x+x^2-x^3, n)[n+1])

a(n) is related to the tribonacci numbers T(n) (A000073) by a(n)=T(n)+2*T(n-1)+3T(n-2).

Cf. A000073.

Adjacent sequences: A001641 A001642 A001643 this_sequence A001645 A001646 A001647

Sequence in context: A064434 A086401 A095732 this_sequence A139123 A133580 A019603

nonn

njas

Edited by Mario Catalani (mario.catalani(AT)unito.it), Jul 17 2002