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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
OFFSET
0,9
COMMENTS
The array is constructed multiplying the even-indexed A026741(k) by 2^n, and keeping the odd-indexed 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.
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^(n-1)*k ; end if; end proc: # R. J. Mathar, Jan 22 2011
CROSSREFS
Sequence in context: A285320 A347710 A340666 * A163575 A355889 A275736
KEYWORD
nonn,easy,tabl
AUTHOR
Paul Curtz, Nov 18 2009
STATUS
approved