|
| |
|
|
A065071
|
|
Minimum number of identical bricks of length 1 which, when stacked without mortar in the naive way, form a stack of length >=n.
|
|
0
| |
|
|
1, 5, 32, 228, 1675, 12368, 91381, 675215, 4989192, 36865413, 272400601, 2012783316, 14872568832, 109894245430, 812014744423, 6000022499694, 44334502845081, 327590128640501, 2420581837980562, 17885814992891027
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| The ratios a(n+1)/a(n) seem to approach e^2=7.389056..., with 7-place agreement for n=11.
Comment from Douglas Rogers, Aug 31, 2005: Note that one can do ''better'' in terms of projections if you group the bricks asymmetrically into lozenges with holes in them. See the Ainsley and Drummond references. Ainsley considers only the case of four bricks, but achieves an overhang of (15-4sqrt2)/8, compared with 25/24 for the harmonic pile.
|
|
|
REFERENCES
| S. Ainley, Letter, Math. Gaz., 63 (1979), 272.
J. E. Drummond, On stacking bricks to achieve a large overhang, Math. Gaz., 65 (1981), 40-42.
N. J. A. Sloane, Illustration for sequence M4299 (=A007340) in The Encyclopedia of Integer Sequences (with S. Plouffe), Academic Press, 1995.
|
|
|
LINKS
| R. Dickau, Harmonic numbers and the book-stacking problem
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics
|
|
|
FORMULA
| Equals A002387(2n) + 1.
|
|
|
EXAMPLE
| Obviously a(1)=1. If the center of gravity of one brick is placed at the end of a second brick, the length of the stack of 2 bricks is 1.5. If the c.g. of that stack is placed at the end of a third brick, the length of the stack is 1.75. Continuing, we get a stack of length 1.916666... for 4 bricks and a stack of length 2.0416666... for 5 bricks. Thus a(2)=5.
|
|
|
MATHEMATICA
| A002387[n_] := Floor[ Exp[n - EulerGamma] + 1/2]; a[n_] := A002387[2n - 2] + 1; a[1] = 1; Table[a[n], {n, 1, 20}] (* From Jean-François Alcover, Dec 13 2011, after Charles R Greathouse IV *)
|
|
|
CROSSREFS
| Cf. harmonic numbers H(n) = A001008/A002805, A002387, A004080.
Sequence in context: A024064 A164594 A199486 * A153396 A146965 A053157
Adjacent sequences: A065068 A065069 A065070 * A065072 A065073 A065074
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Nov 08 2001
|
|
|
EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 14 2001
|
| |
|
|
