

A168068


Array T(n,k) read by antidiagonals: T(n,2k+1) = 2k+1. T(n,2k) = 2^n*k.


2



0, 0, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 4, 3, 2, 0, 1, 8, 3, 4, 5, 0, 1, 16, 3, 8, 5, 3, 0, 1, 32, 3, 16, 5, 6, 7, 0, 1, 64, 3, 32, 5, 12, 7, 4, 0, 1, 128, 3, 64, 5, 24, 7, 8, 9, 0, 1, 256, 3, 128, 5, 48, 7, 16, 9, 5, 0, 1, 512, 3, 256, 5, 96, 7, 32, 9, 10, 11, 0, 1, 1024, 3, 512, 5, 192, 7, 64, 9, 20, 11, 6, 0, 1, 2048, 3, 1024, 5
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,9


COMMENTS

The array is constructed multiplying the evenindexed A026741(k) by 2^n, and keeping the oddindexed A026471(k) as they are.
Connections to the hydrogen spectrum: The squares of the second row are T(1,k)^2 = A001477(k)^2 = A000290(k) which are the denominators of the Lyman lines (see A171522). The squares of the row T(2,k) are in A154615, denominators of the Balmer series. Row T(3,k) is related to A106833 and A061038.


LINKS

Table of n, a(n) for n=0..96.


EXAMPLE

The array starts in row n=0 with columns k>=0 as:
0,1,1,3,2,5,3,7,4, A026741
0,1,2,3,4,5,6,7,8, A001477
0,1,4,3,8,5,12,7,16, A022998
0,1,8,3,16,5,24,7,32, A144433
0,1,16,3,32,5,48,7,64,
0,1,32,3,64,5,96,7,128,


MAPLE

A168068 := proc(n, k) if type(k, 'odd') then k; else 2^(n1)*k ; end if; end proc: # R. J. Mathar, Jan 22 2011


CROSSREFS

Sequence in context: A055137 A143325 A128888 * A163575 A163465 A004443
Adjacent sequences: A168065 A168066 A168067 * A168069 A168070 A168071


KEYWORD

nonn,easy,tabl


AUTHOR

Paul Curtz, Nov 18 2009


STATUS

approved



