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A275778 Tribonacci-like sequence a(n) = a(n-1) + a(n-2) + a(n-3) for n >= 3, with a(0) = 1, a(1) = 2, a(2) = 1. 1
1, 2, 1, 4, 7, 12, 23, 42, 77, 142, 261, 480, 883, 1624, 2987, 5494, 10105, 18586, 34185, 62876, 115647, 212708, 391231, 719586, 1323525, 2434342, 4477453, 8235320, 15147115, 27859888, 51242323, 94249326, 173351537, 318843186, 586444049 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Empirical: constructed from tribonacci sequence reduced mod 3, which has period 13: 0011211102021. It is the fourth sequence; A000073 is the first:

   1: 001 = tribonacci

   2: 011 tribonacci shifted left by 1

   3: 112 tribonacci shifted left by 2

   4: 121 this sequence

   5: 211 ...

   6: 111 ...

   7: 110 ...

   8: 102 ...

   9: 020 ...

  10: 202 ...

  11: 021 ...

  12: 210 ...

  13: 100 ...

Notes about other sequence read modulo 3:

- Fibonacci -> 8-digit periodic sequence

- tribonacci -> 13-digit periodic sequence

- tetranacci -> 26-digit ( 2 * 13 ) periodic sequence

- Padovan/Perrin -> 13-digit periodic sequence

- a(n) = a(n-3) + a(n-4) + a(n-5) -> multiple length periodic sequences using the 242 = 3^5 - 1 ternary combinations available -> (4(2*2), 13, 52(2*2*13), 55 )

These lengths are all Fibonacci numbers or multiples of Fibonacci numbers.

LINKS

Table of n, a(n) for n=0..34.

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

FORMULA

G.f.: (2 x^2-x-1)/(x^3+x^2+x-1).

a(n) = A276658(n) + A000073(n).

MATHEMATICA

CoefficientList[Series[(-1 - x + 2 x^2)/(-1 + x + x^2 + x^3), {x, 0, 35}], x]

RecurrenceTable[{a[n] == a[n - 1] + a[n - 2] + a[n - 3], a[1] == 1, a[2] == 2, a[3] == 1}, a, {n, 35}]

LinearRecurrence[{1, 1, 1}, {1, 2, 1}, 35]

PROG

(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, 1, 1]^n*[1; 2; 1])[1, 1] \\ Charles R Greathouse IV, Sep 10 2016

CROSSREFS

Cf. A000073, A276658

Sequence in context: A217205 A139769 A326894 * A007839 A184345 A045625

Adjacent sequences:  A275775 A275776 A275777 * A275779 A275780 A275781

KEYWORD

nonn,easy

AUTHOR

Nicolas Bègue, Sep 10 2016

STATUS

approved

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Last modified April 6 16:14 EDT 2020. Contains 333276 sequences. (Running on oeis4.)