A123552 Expansion of 1/(1 - x - x^3 + x^5).

1, 1, 1, 2, 3, 3, 4, 6, 7, 8, 11, 14, 16, 20, 26, 31, 37, 47, 58, 69, 85, 106, 128, 155, 192, 235, 284, 348, 428, 520, 633, 777, 949, 1154, 1411, 1727, 2104, 2566, 3139, 3832, 4671, 5706, 6972, 8504, 10378, 12679, 15477, 18883, 23058, 28157, 34361, 41942, 51216, 62519

Offset: 0

Author

Christian G. Bower, Nov 14 2006

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,-1).

Crossrefs

Number of nodes at n-th generation in A123015.

Programs

Mathematica

a=b=c=d=0;Table[e=a+b+1;a=b;b=c;c=d;d=e,{n,100}] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2011*)
CoefficientList[Series[1/(1 - x - x^3 + x^5), {x, 0, 53}], x] (* Michael De Vlieger, Sep 15 2017 *)

PARI

x='x+O('x^99); Vec(1/(1-x-x^3+x^5)) \\ Altug Alkan, Sep 12 2017

Formula

G.f.: 1/((1-x)*(1-x^3-x^4)).

From Robert FERREOL, Sep 12 2017: (Start)

a(n) = a(n-1) + a(n-3) - a(n-5) for n >= 5, with a(0)=a(1)=a(2)=1, a(3)=2, a(4)=3.

a(n) = a(n-3) + a(n-4) + 1 for n >= 4, with a(0)=a(1)=a(2)=1, a(3)=2.

a(n) - a(n-1) = A017817(n). (End)