A192395 a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) + 2*a(n-4) starting with a(0..3) = 0, 0, 0, 1.

0, 0, 0, 1, 2, 2, 1, 2, 8, 17, 22, 22, 33, 78, 156, 233, 298, 442, 833, 1546, 2464, 3553, 5390, 9230, 16161, 26358, 40404, 62713, 103298, 174290, 285505, 451154, 712184, 1156145, 1910086, 3122374, 5005089, 7987806, 12907980, 21090185, 34362394, 55428010

Offset: 0

Author

Paul Curtz, Jun 29 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-2,1,2).

Crossrefs

Cf. A000045, A107920.

Programs

Magma

I:=[0,0,0,1]; [n le 4 select I[n] else 2*Self(n-1)-2*Self(n-2)+Self(n-3)+2*Self(n-4): n in [1..50]]; // Vincenzo Librandi, Nov 25 2011

Maple

a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <2|1|-2|2>>^n)[1,4]:
seq(a(n), n=0..45);  # Alois P. Heinz, Jul 11 2023

Mathematica

LinearRecurrence[{2,-2,1,2},{0,0,0,1},100] (* Vincenzo Librandi, Nov 25 2011 *)

SageMath

@CachedFunction
def a(n): # a = A192395
    if (n<4): return n//3
    else: return 2*a(n-1) - 2*a(n-2) + a(n-3) + 2*a(n-4)
[a(n) for n in range(51)] # G. C. Greubel, Jul 10 2023

Formula

From R. J. Mathar, Jul 14 2011: (Start)

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

a(n) = (A000045(n) - A107920(n))/3. (End)