A141525 a(n) = a(n-2) + a(n-3) if n == 0 (mod 3), a(n-1) + a(n-4) if n == 0 (mod 4), otherwise a(n-2) with a(0) = 0 and a(1) = a(2) = a(3) = 1.

0, 1, 1, 1, 1, 1, 2, 2, 3, 4, 4, 4, 8, 8, 8, 16, 24, 24, 40, 40, 64, 80, 80, 80, 160, 160, 160, 320, 480, 480, 800, 800, 1280, 1600, 1600, 1600, 3200, 3200, 3200, 6400, 9600, 9600, 16000, 16000, 25600, 32000, 32000, 32000, 64000, 64000, 64000, 128000, 192000, 192000, 320000, 320000, 512000, 640000, 640000, 640000, 1280000

Offset

0,7

Comments

Lim_{n -> infinity} <a(n+1)/a(n)> = 1.324717957244746, where <> is the expectation value.

References

.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Mathematica

a[n_]:= a[n]= If[n==0, 0, If[n<4, 1, If[Mod[n, 3]==0, a[n-2] + a[n-3], If[Mod[n, 4] ==0, a[n-1] + a[n-4], a[n-1] ]]]];
Table[a[n], {n, 0, 65}] (* modified by G. C. Greubel, Mar 29 2021 *)

Prog

(Magma)
function a(n)
  if n eq 0 then return 0;
  elif n lt 4 then return 1;
  elif (n mod 3) eq 0 then return a(n-2) + a(n-3);
  elif (n mod 4) eq 0 then return a(n-1) + a(n-4);
  else return a(n-1);
  end if; return a;
end function;
[a(n): n in [0..65]]; // G. C. Greubel, Mar 29 2021
(Sage)
@CachedFunction
def a(n):
    if (n==0): return 0
    elif (n<4): return 1
    elif (n%3==0): return a(n-2) + a(n-3)
    elif (n%4==0): return a(n-1) + a(n-4)
    else: return a(n-1)
[a(n) for n in (0..65)] # G. C. Greubel, Mar 29 2021

Crossrefs

Sequence in context: A049980 A359897 A209698 * A209764 A071475 A358104

Adjacent sequences: A141522 A141523 A141524 * A141526 A141527 A141528

Keyword

nonn

Author

Roger L. Bagula, Aug 11 2008

Extensions

Edited by G. C. Greubel, Mar 29 2021

Status

approved