A045626 Bends in loxodromic sequence of spheres in which each 5 consecutive spheres are in mutual contact.

-1, 2, 3, 3, 5, 14, 23, 42, 81, 155, 287, 542, 1023, 1926, 3623, 6827, 12857, 24210, 45591, 85862, 161693, 304499, 573435, 1079898, 2033663, 3829802, 7212299, 13582227, 25578093, 48168758, 90711575, 170828354

Offset

0,2

References

H. S. M. Coxeter, 5 spheres in mutual contact, Abstracts AMS 18 (1997), p. 431, #924-05-202; also Math. Intell. 19(4) 1997 pp. 41-47.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: -(1-3*x-2*x^2+x^3+2*x^4)/((1+x)*(1-2*x+x^2-2*x^3+x^4)) (conjectured). - Ralf Stephan, May 06 2004

Maple

a:= proc(n) option remember;
  if n=0 then -1
  elif n=1 then 2
  elif n<=3 then 3
  elif n=4 then 5
  else a(n-1)+a(n-2)+a(n-3)+a(n-4)-a(n-5);
  fi; end;
seq(a(n), n=0..40);

Mathematica

a[n_]:= a[n]= If[n==0, -1, If[n<3, n+1, If[n<5, 2*n-3, a[n-1] +a[n-2] +a[n-3] +a[n-4] -a[n-5]]]]; Table[a[n], {n, 0, 40}] (* G. C. Greubel, Jan 13 2020 *)

Prog

(PARI) a(n) = if(n==0, -1, if(n<3, n+1, if(n<5, 2*n-3, a(n-1) +a(n-2) +a(n-3) +a(n-4) -a(n-5) )));
vector(41, n, a(n-1)) \\ G. C. Greubel, Jan 13 2020
(Magma) I:=[-1, 2, 3, 3, 5]; [n le 5 select I[n] else Self(n-1) +Self(n-2) +Self(n-3) +Self(n-4) -Self(n-5): n in [1..40]]; // G. C. Greubel, Jan 13 2020
(Sage)
@CachedFunction
def a(n):
    if (n==0): return -1
    elif (n<3): return n+1
    elif (n<5): return 2*n-3
    else: return a(n-1)+a(n-2)+a(n-3)+a(n-4)-a(n-5)
[a(n) for n in (0..40)] # G. C. Greubel, Jan 13 2020
(GAP) a:=[-1, 2, 3, 3, 5];; for n in [6..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]+a[n-4] -a[n-5]; od; a; # G. C. Greubel, Jan 13 2020

Crossrefs

Sequence in context: A064339 A174010 A053199 * A275914 A154923 A154693

Adjacent sequences: A045623 A045624 A045625 * A045627 A045628 A045629

Keyword

sign

Author

N. J. A. Sloane

Status

approved