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A086192 Tribonacci numbers that start with first three squares. 2
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 (list; graph; refs; listen; history; text; internal format)
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, RafaƂ 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).

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). [From R. J. Mathar, Apr 20 2009]

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. A000213.

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

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Last modified June 30 08:42 EDT 2022. Contains 354919 sequences. (Running on oeis4.)