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

Author

Paul Barry, Aug 30 2004

Keywords

• easy
• nonn

Comments

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

Links

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

Crossrefs

Cf. A000213, A098182, A098183.

Programs

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 *)

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

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

Formula

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

a(n) = Sum_{k=0..floor(n/2)} binomial(n+k, 3*k)*4^k.

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