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A121546 a(n) = dimension of the space in which the sphere of radius n is of maximum volume. 0
5, 24, 56, 100, 156, 225, 307, 401, 508, 627, 759, 904, 1061, 1231, 1413, 1607, 1815, 2035, 2267, 2512, 2770, 3040, 3323, 3618, 3926, 4246, 4579, 4925, 5283, 5654, 6037, 6433, 6841, 7262, 7696, 8142, 8601, 9072, 9556, 10052, 10561, 11083, 11617, 12163 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..44.

John Moeller, Reasoning in Higher Dimensions: Hyperspheres, onTopology Blog, 3 March 2009.

FORMULA

a(n) >= 6.2835n^2 - 0.009903n - 0.9212 is a lower bound on the real value of the dimension.

MAPLE

N:= 10^5: # to get all terms <= N

G[1]:= 2/Pi:

G[2]:= 3/4:

L[2]:= 0:

for n from 3 to N do

  G[n]:= G[n-2]*(n+1)/n;

  L[n]:= floor(G[n]);

  if L[n] <> L[n-1] then

     A[L[n]]:= n

  fi

od:

seq(A[i], i=1..L[N]); # Robert Israel, Jan 05 2016

MATHEMATICA

vol[n_, r_]:=If[IntegerQ[n/2], (Pi^(n/2)*r^n)/(n/2)!, (Pi^((n-1)/2)*((n+1)/2)!*2^(n+1)*r^n)/(n+1)!];

dim[r_]:=Block[{d=1}, While[vol[d, r]<vol[d+1, r], d++]; d];

dim/@Range@30 (* Ivan N. Ianakiev, Dec 27 2015 *)

PROG

(PARI) V(d, r)=Pi^(d/2)*r^d/gamma(d/2+1)

a(n)=my(d=ceil(6.2835*n^2-0.009903*n-0.9212)); while(V(d, n)<V(d-1, n), d--); while(V(d, n)<V(d+1, n), d++); d \\ Charles R Greathouse IV, Mar 06 2014

CROSSREFS

Sequence in context: A219509 A202326 A085646 * A135703 A258290 A205669

Adjacent sequences:  A121543 A121544 A121545 * A121547 A121548 A121549

KEYWORD

nonn

AUTHOR

Sergio Falcon, Oct 10 2007

STATUS

approved

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Last modified October 16 06:21 EDT 2019. Contains 328048 sequences. (Running on oeis4.)