A145682 - OEIS

%I #3 May 01 2013 21:05:52

%S 2,8,32,113,382,833,1822,3713,7582

%N The value of the sum shown in the display appears to 2, 8, 32 - sqrt(2), 113, 382, 833, 1822, 3713, 7582, ... for n = 1, ..., 9.

%C This is an unusual sequence mentioned on the Math Fun Mailing list. It does not quite fit the format of regular OEIS entries, but is too interesting to be forgotten. - _N. J. A. Sloane_, Mar 29 2009

%C The definition arises from the Fourier series for the Snowflake curve.

%C ..................................................................

%C .............................. inf ...............................

%C .............................. ==== ............ m ...............

%C ............................ k \ ....... %pi (k 2..- 5) ..... n ..

%C ....................... (- 1).. > .. tan(--------------) (- 1) ...

%C ............. inf ............ / ............ n + m ..............

%C ............. ==== ........... ==== ........ 2 ...................

%C ..... 5 m - 1 \ .............. n = 1 .............................

%C .. 3 2 ....... > ...... --------------------------------------- ..

%C ............. / .................................... m ...........

%C ............. ==== .......... m ... 3 ... 10 %pi (k 2 .- 5) ......

%C ............. k = - inf . (k 2..- 5)..csc(-----------------) .....

%C ................................................ 2 m .............

%C ............................................... 2 ................

%C .. ------------------------------------------------------------ ..

%C ........................... 3 ... 5 %pi ..........................

%C ........................ %pi..csc(-----) .........................

%C ................................... m ............................

%C .................................. 2 .............................

%K nonn

%O 1,1

%A _Bill Gosper_, Apr 12 2005