A277253 a(n) = a(n-2) + a(n-3) + a(n-4) for n>3, a(0)=1, a(1)=a(2)=0, a(3)=2.

1, 0, 0, 2, 1, 2, 3, 5, 6, 10, 14, 21, 30, 45, 65, 96, 140, 206, 301, 442, 647, 949, 1390, 2038, 2986, 4377, 6414, 9401, 13777, 20192, 29592, 43370, 63561, 93154, 136523, 200085, 293238, 429762, 629846, 923085, 1352846, 1982693, 2905777, 4258624, 6241316, 9147094, 13405717, 19647034, 28794127, 42199845

Offset: 0

Author

Nicolas Bègue, Oct 07 2016

Keywords

• nonn
• easy

Comments

a(n+1)/a(n) = 1.465571... like Narayana's cows sequence A000930.

Links

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

Crossrefs

Cf. A000930.

Programs

Magma

I:=[1,0,0,2]; [n le 4 select I[n] else Self(n-2)+Self(n-3)+Self(n-4): n in [1..50]]; // Vincenzo Librandi, Nov 07 2016

Maple

a:= n-> (<<0|1|0|0>, <0|0|1|0>,
          <0|0|0|1>, <1|1|1|0>>^n. <<1,0,0,2>>)[1,1]:
seq(a(n), n=0..50);  # Alois P. Heinz, Oct 07 2016

Mathematica

RecurrenceTable[{a[n] == a[n - 2] + a[n - 3] + a[n - 4], a[1] ==1,  a[2] == a[3] == 0, a[4] == 2}, a, {n, 50}]
LinearRecurrence[{0, 1, 1, 1}, {1, 0, 0, 2}, 52]
CoefficientList[Series[(-1 + x^2 - x^3)/(-1 + x^2 + x^3 + x^4), {x, 0, 52}], x]
nxt[{a_,b_,c_,d_}]:={b,c,d,a+b+c}; NestList[nxt,{1,0,0,2},50][[;;,1]] (* Harvey P. Dale, Jun 10 2023 *)

Formula

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