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A152714 Triangle read by rows: T(n,k) = 3^min(k, n-k). 5

%I

%S 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,

%T 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,

%U 81,27,9,3,1

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

%H G. C. Greubel, <a href="/A152714/b152714.txt">Rows n=0..100 of triangle, flattened</a>

%F T(n,k) = 3^min(k, n-k) = 3^A004197(n,k). - _Philippe Deléham_, Feb 25 2014

%e Triangle begins

%e {1},

%e {1, 1},

%e {1, 3, 1},

%e {1, 3, 3, 1},

%e {1, 3, 9, 3, 1},

%e {1, 3, 9, 9, 3, 1},

%e {1, 3, 9, 27, 9, 3, 1},

%e {1, 3, 9, 27, 27, 9, 3, 1},

%e {1, 3, 9, 27, 81, 27, 9, 3, 1},

%e {1, 3, 9, 27, 81, 81, 27, 9, 3, 1},

%e {1, 3, 9, 27, 81, 243, 81, 27, 9, 3, 1}

%t Clear[a, k, m]; k = 3; 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[%]

%t Table[3^(Min[k, n - k]), {n, 0, 100}, {k, 0, n}] // Flatten (* _G. C. Greubel_, Sep 01 2018 *)

%o (PARI) for(n=0,15, for(k=0,n, print1(3^(min(k,n-k)), ", "))) \\ _G. C. Greubel_, Sep 01 2018

%o (MAGMA) [[3^(Min(k,n-k)): k in [0..n]]: n in [0..15]]; // _G. C. Greubel_, Sep 01 2018

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

%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

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Last modified June 16 19:49 EDT 2021. Contains 345068 sequences. (Running on oeis4.)