A098184 a(n) = 3a(n-1)+a(n-2)+a(n-3), a(0)=1, a(1)=1, a(2)=5.

1, 1, 5, 17, 57, 193, 653, 2209, 7473, 25281, 85525, 289329, 978793, 3311233, 11201821, 37895489, 128199521, 433695873, 1467182629, 4963443281, 16791208345, 56804250945, 192167404461, 650097672673, 2199264673425

Offset

0,3

Comments

Even bisection of the tribonacci sequence A000213. - Oboifeng Dira, Aug 03 2016

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (3,1,1).

Formula

G.f.: (1-x)^2/(1-3x-x^2-x^3); a(n)=sum(k=0..floor(n/2), binomial(n+k, 3k)4^k}.

a(n)/a(n-1) tends to 3.38297576..., the square of the tribonacci constant A058265. - Gary W. Adamson, Feb 28 2006

Mathematica

LinearRecurrence[{3, 1, 1}, {1, 1, 5}, 30] (* Harvey P. Dale, Nov 29 2011 *)
CoefficientList[Series[(1 - x)^2/(1 - 3 x - x^2 - x^3), {x, 0, 24}], x] (* Michael De Vlieger, Aug 03 2016 *)

Prog

(Sage)
from sage.combinat.sloane_functions import recur_gen3
it = recur_gen3(1, 1, 1, 3, 1, 1)
[next(it) for i in range(32)] # Zerinvary Lajos, Jun 24 2008
(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, 1, 3]^n*[1; 1; 5])[1, 1] \\ Charles R Greathouse IV, Aug 03 2016

Crossrefs

Cf. A000213, A098182, A098183.

Sequence in context: A027095 A027034 A027097 * A289590 A054113 A146697

Adjacent sequences: A098181 A098182 A098183 * A098185 A098186 A098187

Keyword

easy,nonn

Author

Paul Barry, Aug 30 2004

Status

approved