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

1,1

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

Links

Table of n, a(n) for n=1..9.

Crossrefs

Sequence in context: A052481 A306292 A067897 * A363109 A289451 A230509

Adjacent sequences: A145679 A145680 A145681 * A145683 A145684 A145685

Keyword

nonn

Author

Bill Gosper, Apr 12 2005

Status

approved