A213944 - OEIS

%I #15 Mar 06 2013 06:58:00

%S 1,2,0,3,2,0,3,4,0,0,3,6,3,0,0,3,6,6,0,0,0,3,6,9,4,0,0,0,3,6,9,8,0,0,

%T 0,0,3,6,9,12,5,0,0,0,0,3,6,9,12,10,0,0,0,0,0,3,6,9,12,15,6,0,0,0,0,0,

%U 3,6,9,12,15,12

%N Triangle read by rows, with column k defined by partial sums of the finite sequence that contains k three times.

%H Harvey P. Dale, <a href="/A213944/b213944.txt">Table of n, a(n) for n = 1..10000</a>

%F T(n,k) = 0 if 2k > n+1. T(n,k) = k if 2k=n+1. T(n,k)=2k if 2k=n. T(n,k) = 3k if 2k <= n-1.

%e First few rows of the triangle are:

%e 1;

%e 2, 0;

%e 3, 2, 0;

%e 3, 4, 0, 0;

%e 3, 6, 3, 0, 0;

%e 3, 6, 6, 0, 0, 0;

%e 3, 6, 9, 4, 0, 0, 0;

%e 3, 6, 9, 8, 0, 0, 0, 0;

%e 3, 6, 9, 12, 5, 0, 0, 0, 0;

%e 3, 6, 9, 12, 10, 0, 0, 0, 0, 0;

%e 3, 6, 9, 12, 15, 6, 0, 0, 0, 0, 0;

%e 3, 6, 9, 12, 15, 12, 0, 0, 0, 0, 0, 0;

%e ...

%t fs[n_,k_]:=Which[2k>n+1,0,2k==n+1,k,2k==n,2k,2k<=n-1,3k]; Flatten[ Table[ fs[n,k],{n,15},{k,n}]] (* _Harvey P. Dale_, Mar 06 2013 *)

%Y Cf. A001318 (row sums)

%K nonn,tabl,less,easy

%O 1,2

%A _Gary W. Adamson_, Jun 25 2012