A086192 Tribonacci numbers that start with first three squares.

1, 4, 9, 14, 27, 50, 91, 168, 309, 568, 1045, 1922, 3535, 6502, 11959, 21996, 40457, 74412, 136865, 251734, 463011, 851610, 1566355, 2880976, 5298941, 9746272, 17926189, 32971402, 60643863, 111541454, 205156719, 377342036, 694040209

Offset

1,2

Comments

n and a(n) are of the same parity. Except for the first three terms and a(5)=27, there is no perfect powers (A001597) in the first 225 terms. In fact there is always at least one factor which is represented only once. - Robert G. Wilson v, Aug 27 2003

Links

Table of n, a(n) for n=1..33.

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

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

Formula

a(n) = a(n-1) + a(n-2) + a(n-3).

From R. J. Mathar, Apr 20 2009: (Start(

a(n) = 4*A000073(n) + 3*A000073(n-1) + A000073(n-2).

G.f.: -x*(1+3*x+4*x^2)/(-1+x+x^2+x^3). (End)

Mathematica

a[1] = 1; a[2] = 4; a[3] = 9; a[n_] := a[n] = a[n - 3] + a[n - 2] + a[n - 1]; Table[ a[n], {n, 1, 30}]
Transpose[NestList[Flatten[{Rest[#], Total[#]}]&, {1, 4, 9}, 40]][[1]] (* Harvey P. Dale, Mar 24 2011 *)
LinearRecurrence[{1, 1, 1}, {1, 4, 9}, 33] (* Ray Chandler, Dec 08 2013 *)

Crossrefs

Cf. A000073, A000213, A001597.

Sequence in context: A004630 A073497 A244941 * A105503 A095169 A345407

Adjacent sequences: A086189 A086190 A086191 * A086193 A086194 A086195

Keyword

nonn,easy

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Aug 26 2003

Extensions

More terms from Robert G. Wilson v, Aug 27 2003

Status

approved