login
Triangle T(n,k) read by rows: T(n,k) = 4^min(k, n-k) = 4^A004197(n,k).
6

%I #10 Feb 26 2014 10:29:28

%S 1,1,1,1,4,1,1,4,4,1,1,4,16,4,1,1,4,16,16,4,1,1,4,16,64,16,4,1,1,4,16,

%T 64,64,16,4,1,1,4,16,64,256,64,16,4,1,1,4,16,64,256,256,64,16,4,1,1,4,

%U 16,64,256,1024,256,64,16,4,1

%N Triangle T(n,k) read by rows: T(n,k) = 4^min(k, n-k) = 4^A004197(n,k).

%C Row sums are: {1, 2, 6, 10, 26, 42, 106, 170, 426, 682, 1706,...} = A061547(n+2).

%F T(n,k) = 4^min(k, n-k). - _Philippe Deléham_, Feb 25 2014

%F T(n,k) = A144464(n,k)^2. - _Philippe Deléham_, Feb 26 2014

%e {1},

%e {1, 1},

%e {1, 4, 1},

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

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

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

%e {1, 4, 16, 64, 16, 4, 1},

%e {1, 4, 16, 64, 64, 16, 4, 1},

%e {1, 4, 16, 64, 256, 64, 16, 4, 1},

%e {1, 4, 16, 64, 256, 256, 64, 16, 4, 1},

%e {1, 4, 16, 64, 256, 1024, 256, 64, 16, 4, 1}

%t Clear[a, k, m]; k = 4; a[0] = {1}; a[1] = {1, 1};

%t a[n_] := a[n] = Join[{1}, k*a[n - 2], {1}];

%t Table[a[n], {n, 0, 10}];

%t Flatten[%]

%Y Cf. A004197, A144464, A152714, A152717.

%K nonn,easy,tabl

%O 0,5

%A _Roger L. Bagula_ and _Gary W. Adamson_, Dec 11 2008

%E Better name by _Philippe Deléham_, Feb 25 2014