A106314 - OEIS

%I #8 Jan 25 2017 05:41:44

%S 1,1,1,1,4,1,1,4,4,1,1,4,9,4,1,1,4,9,9,4,1,1,4,9,16,9,4,1,1,4,9,16,16,

%T 9,4,1,1,4,9,16,25,16,9,4,1,1,4,9,16,25,25,16,9,4,1

%N Triangle T(n,k) composed of the squares min(n,k)^2.

%F T(n,k) = A003983(n,k)^2.

%e Replacing each term in A003983 by its square, we get:

%e {1},

%e {1, 1},

%e {1, 4, 1},

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

%e {1, 4, 9, 4, 1},

%e {1, 4, 9, 9, 4, 1},

%e {1, 4, 9, 16, 9, 4, 1},

%e {1, 4, 9, 16, 16, 9, 4, 1},

%e {1, 4, 9, 16, 25, 16, 9, 4, 1},

%e {1, 4, 9, 16, 25, 25, 16, 9, 4, 1},

%e {1, 4, 9, 16, 25, 36, 25, 16, 9, 4, 1}

%t Clear[p, n, i];

%t p[x_, n_] = Sum[x^i*If[i ==Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= Floor[n/2], 2*i + 1, -(2*(n - i) + 1)]], {i, 0, n}]/(1 - x);

%t Table[CoefficientList[FullSimplify[p[x, n]], x], {n, 1, 11}];

%t Flatten[%]

%Y Cf. A003983, A106314, A005993 (row sums).

%K nonn,tabl,easy

%O 1,5

%A _Gary W. Adamson_, Apr 28 2005

%E Additional comments from _Roger L. Bagula_ and _Gary W. Adamson_, Apr 02 2009