A145682 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.

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

Offset: 1

Author

Bill Gosper, Apr 12 2005

Keywords

• nonn

Comments

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

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

..................................................................

.............................. inf ...............................

.............................. ==== ............ m ...............

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

....................... (- 1).. > .. tan(--------------) (- 1) ...

............. inf ............ / ............ n + m ..............

............. ==== ........... ==== ........ 2 ...................

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

.. 3 2 ....... > ...... --------------------------------------- ..

............. / .................................... m ...........

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

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

................................................ 2 m .............

............................................... 2 ................

.. ------------------------------------------------------------ ..

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

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

................................... m ............................

.................................. 2 .............................