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 A045626 Bends in loxodromic sequence of spheres in which each 5 consecutive spheres are in mutual contact. 1
 -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 (list; graph; refs; listen; history; text; internal format)
 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 STATUS approved

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Last modified March 28 11:49 EDT 2020. Contains 333083 sequences. (Running on oeis4.)