A276228 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A276228

a(n+3) = -a(n+2) - 2*a(n+1) + a(n) with a(0)=3, a(1)=-1, a(2)=-3.

3, -1, -3, 8, -3, -16, 30, -1, -75, 107, 42, -331, 354, 350, -1389, 1043, 2085, -5560, 2433, 10772, -21198, 2087, 51081, -76453, -23622, 227609, -256818, -222022, 963267, -776041, -1372515, 3887864, -1918875, -7229368, 14954982, -2415121, -34724211, 54509435, 12523866

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..4925

Yüksel Soykan, Summing Formulas For Generalized Tribonacci Numbers, arXiv:1910.03490 [math.GM], 2019.

Index entries for linear recurrences with constant coefficients, signature (-1,-2,1).

FORMULA

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

Let (b, c, d) be the three roots of x^3 = 2*x^2 + x + 1, then a(n) = b^(-n) + c^(-n) + d^(-n) = A276225(-n).

a(2*n) = -3*a(2*n-2) - 6*a(2*n-4) + a(2*n-6).

a(n) = 2*A276229(n) + 2*A276229(n+1) + 3*A276229(n+2).

MATHEMATICA

LinearRecurrence[{-1, -2, 1}, {3, -1, -3}, 50]

CoefficientList[Series[(3 + 2 x + 2 x^2)/(1 + x + 2 x^2 - x^3), {x, 0, 38}], x] (* Michael De Vlieger, Aug 25 2016 *)

nxt[{a_, b_, c_}]:={b, c, a-2b-c}; NestList[nxt, {3, -1, -3}, 40][[All, 1]] (* Harvey P. Dale, Dec 19 2022 *)

PROG

(Magma) I:=[3, -1, -3]; [n le 3 select I[n] else -Self(n-1)- 2*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Aug 25 2016

(PARI) Vec((3+2*x+2*x^2)/(1+x+2*x^2-x^3) + O(x^99)) \\ Altug Alkan, Aug 25 2016

CROSSREFS

Cf. A276225, A276229.

Sequence in context: A046544 A011088 A352794 * A188938 A156368 A240665

Adjacent sequences: A276225 A276226 A276227 * A276229 A276230 A276231

KEYWORD

sign,easy

AUTHOR

G. C. Greubel, Aug 24 2016

EXTENSIONS

Deleted certain dangerous or potentially dangerous links. - N. J. A. Sloane, Jan 30 2021

STATUS

approved