A121959 a(n) = (n-3)*a(n-1) + a(n-4), with a(1)=0, a(2)=1, a(3)=2, a(4)=3.

0, 1, 2, 3, 6, 19, 78, 393, 2364, 16567, 132614, 1193919, 11941554, 131373661, 1576616546, 20497209017, 286972867792, 4304724390541, 68877166865202, 1170932333917451, 21077068983381910, 400468615408646831

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..450

Maple

a:= proc(n) option remember;
      if n<5 then n-1
    else (n-3)*a(n-1) + a(n-4)
      fi;
    end:
seq(a(n), n=1..30); # G. C. Greubel, Oct 05 2019

Mathematica

(* First program *)
M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, n}}; v[1] = {0, 1, 2, 3};
v[n_] := v[n]= M.v[n-1]; Table[Floor[v[n][[1]]], {n, 30}]
Det[M - x*IdentityMatrix[4]]
(* Second program *)
a[n_]:= a[n] = If[n<5, n-1, (n-3)*a[n-1] + a[n-4]]; Table[a[n], {n, 30}] (* G. C. Greubel, Oct 05 2019 *)

Prog

(PARI) my(m=30, v=concat([0, 1, 2, 3], vector(m-4))); for(n=5, m, v[n]=(n-3)*v[n-1] +v[n-4]); v \\ G. C. Greubel, Oct 05 2019
(Magma) I:=[0, 1, 2, 3]; [n le 4 select I[n] else (n-3)*Self(n-1) + Self(n-4): n in [1..30]]; // G. C. Greubel, Oct 05 2019
(Sage)
def a(n):
    if (n<5): return n-1
    else: return (n-3)*a(n-1) + a(n-4)
[a(n) for n in (1..30)] # G. C. Greubel, Oct 05 2019
(GAP)
a:= function(n)
    if n<5 then return n-1;
    else return (n-3)*a(n-1) + a(n-4);
    fi;
  end;
List([1..30], n-> a(n) ); # G. C. Greubel, Oct 05 2019

Crossrefs

Sequence in context: A018290 A364645 A182250 * A075633 A141048 A326030

Adjacent sequences: A121956 A121957 A121958 * A121960 A121961 A121962

Keyword

nonn

Author

Roger L. Bagula, Sep 02 2006

Extensions

Definition replaced with recurrence by the Assoc. Eds. of the OEIS, Mar 27 2010

Status

approved