A152714 Triangle read by rows: T(n,k) = 3^min(k, n-k).

1, 1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 3, 9, 3, 1, 1, 3, 9, 9, 3, 1, 1, 3, 9, 27, 9, 3, 1, 1, 3, 9, 27, 27, 9, 3, 1, 1, 3, 9, 27, 81, 27, 9, 3, 1, 1, 3, 9, 27, 81, 81, 27, 9, 3, 1, 1, 3, 9, 27, 81, 243, 81, 27, 9, 3, 1

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Dec 11 2008

Keywords

• nonn
• easy
• tabl

Examples

			Triangle begins
  {1},
  {1, 1},
  {1, 3, 1},
  {1, 3, 3,  1},
  {1, 3, 9,  3,  1},
  {1, 3, 9,  9,  3,   1},
  {1, 3, 9, 27,  9,   3,  1},
  {1, 3, 9, 27, 27,   9,  3,  1},
  {1, 3, 9, 27, 81,  27,  9,  3, 1},
  {1, 3, 9, 27, 81,  81, 27,  9, 3, 1},
  {1, 3, 9, 27, 81, 243, 81, 27, 9, 3, 1}
		

Links

• G. C. Greubel, Rows n=0..100 of triangle, flattened

Crossrefs

Cf. A004197, A144464, A152716, A152717, A062318 (row sums).

Programs

Magma

[[3^(Min(k,n-k)): k in [0..n]]: n in [0..15]]; // G. C. Greubel, Sep 01 2018

Mathematica

Clear[a, k, m]; k = 3; a[0] = {1}; a[1] = {1, 1};
a[n_] := a[n] = Join[{1}, k*a[n - 2], {1}];
Table[a[n], {n, 0, 10}];
Flatten[%]
Table[3^(Min[k, n - k]), {n, 0, 100}, {k, 0, n}] // Flatten (* G. C. Greubel, Sep 01 2018 *)

PARI

for(n=0,15, for(k=0,n, print1(3^(min(k,n-k)), ", "))) \\ G. C. Greubel, Sep 01 2018

Formula

T(n,k) = 3^min(k, n-k) = 3^A004197(n,k). - Philippe Deléham, Feb 25 2014

Extensions

Better name by Philippe Deléham, Feb 25 2014