login
Triangle T(n,m) read by rows: T(n,m) = 2^min(m,n-m).
8

%I #13 Feb 25 2014 06:52:58

%S 1,1,1,1,2,1,1,2,2,1,1,2,4,2,1,1,2,4,4,2,1,1,2,4,8,4,2,1,1,2,4,8,8,4,

%T 2,1,1,2,4,8,16,8,4,2,1,1,2,4,8,16,16,8,4,2,1,1,2,4,8,16,32,16,8,4,2,1

%N Triangle T(n,m) read by rows: T(n,m) = 2^min(m,n-m).

%F Row sums: sum_{m=0..n} T(n,m) = A027383(n).

%F T(n,k) = 2^A004197(n,k). - _Philippe Deléham_, Feb 25 2014

%e The triangle starts in row n=0 as:

%e {1},

%e {1, 1},

%e {1, 2, 1},

%e {1, 2, 2, 1},

%e {1, 2, 4, 2, 1},

%e {1, 2, 4, 4, 2, 1},

%e {1, 2, 4, 8, 4, 2, 1},

%e {1, 2, 4, 8, 8, 4, 2, 1},

%e {1, 2, 4, 8, 16, 8, 4, 2, 1},

%e {1, 2, 4, 8, 16, 16, 8, 4, 2, 1},

%e {1, 2, 4, 8, 16, 32, 16, 8, 4, 2, 1}

%t Clear[f, t]; f[n_, m_] = If[m <= Floor[n/2], m, n - m]; Table[Table[f[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

%o (PARI) T(n,m)=1<<min(m,n-m) \\ _Charles R Greathouse IV_, Jan 15 2012

%Y Cf. A004197, A152714, A152716, A152717.

%K nonn,easy,tabl

%O 0,5

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 09 2008

%E Offset corrected by the Associate Editors of the OEIS, Sep 11 2009

%E Better name by _Philippe Deléham_, Feb 25 2014